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Eliminate the Parameter XYZ Plane-Video
Dot Product of AxB Vectors-Video
Divergance at a Point Curl Solver-Video
Disk Method Revolving Around Y Axis- Video
Disk Method Solver-Video
Triple or Multiple Integral dx,dy,dz-Video
Triple Integral calculator example dx dy dz
Full Video Transcript
Hello again everybody this is Tom from everystepcalculus.com everystepphysics.com. This time calculus triple integral with the order of integration dx dy dz. Let’s do an index8() to get to my menu.
We’re at triple integrals already XYZ. And we’re going to enter the function alpha first before you enter anything in these entry lines, remember that. Alpha x squared plus y squared plus Z squared.
It always asks if it’s ok so that you can change it in case you made a mistake. And we’re going to want to do number 1 dx dy dz. There’s the region. So our limits of integration alpha 0 alpha 1 okay? Alpha minus 2 alpha 4 okay? Alpha 2, alpha 5.
Again here they are , notice that you’re going to do dx dy dz you’re going to do with respect to X first. Integrate this with respect to x, then y, then z. Here’s the x limits here’s the y limits, here’s the z limits.
So with respect to X here’s the answer here and then over 1 over 0 at x equals 1 this is the answer here. You put…remember to put parentheses around these instead I have to put quotation because of the program but i’d rather have parentheses. I want you to put parentheses around these quotation marks because you’re substituting something in for a variable that’s the way you do it in math.
And then the upper minus the lower so here’s the answer for that respect to x. Now we’re going to integrate that and then over these limits. So the integration of this with respect to y is this right here. And then over 4 minus 2 at 4 ,this is the answer. At minus 2 this is the answer.
Now upper- lower and we have this right here now we’re going to integrate that. dz with respect to z and over 5 and 2 here’s the integral of that. And now a limits at Z equals 5 here they are here’s the is the answer 380. And C equals 2 here’s the answer 68.
Now upper- lower answers is 312 cubic units. Pretty neat huh try that by memory try to do that by memory on a test very difficult, let alone a week after you get out of calculus, you won’t remember this forever . Have a good one!
More Triple Integral videos
Triple Integral calculator example #1
Double Integral Limits of Integration-Video
Integration by Parts Sine-Video
Raw Transcript
Hello, everyone. Tom from everystepcalculus.com and everystepphyics.com. A problem in calculus.
Integration by Parts. Let’s do it. Sine. So let’s do it. Scroll down to integration by parts. I’m already there to save time. It’s called Integrate transcendentals. And we’re going to choose number 3, Sine. And we’re going to enter our function. You have to press Alpha before you enter anything into these entry lines, here. Alpha x times sine of 3 times, make sure you add the times sign between in math, it’s a good practice. Not only for my programs but for any program or anything in the calculator. You have to tell the calculator and me what you want. Not just do what professors do on the blackboard. which is put 3x. I always show you’ve entered, you can change it if you want. I say it’s okay. And dv then is the sine of 3x and the integral of sine of 3x is this minus cosine 3x divided by 3 and that’s v. Should be a plus c. I don’t know integration by parts. There is a plus 3 c after this but the geniuses in Calculus just kind of throw that off and I don’t why. And x is the u and the derivative of x is one. So now the formula v times u minus the integral of v times du dx. A lot of books have u times v. I like to put it v times u because here we have v times du so we have the same. So we add, you add that v minus cosine of 3x divided by 3 times x. And the integral of v which is v, here’s v again and then du is one. So you just add the things to the formula, which we’re doing here. And this turns out to be this minus the cosine of 3x divided by 3 and then we have the same thing in here. Anytime you have a constant in the integral, you take it out. So here’s the, take the one third out of the integral and then integrate minus cosine of 3x. And minus x times cosine of 3 x is equal to minus one third minus the sine of 3x divided by 3. Now we bring the third out here again and that’s where you get the one ninth. So the answer is this minus x cosine of 3 divided by 3 and here’s one ninth times sine of 3x plus C. Pretty neat, huh? Have a good one.
Double Integral Limits of Integration-Video
Raw Transcript
Hello, Tom from everystepcalculus.com and everystepphysics.com. Double Integral today. On this video. Um, so let’s do it. Index 8 to get to my menu. We’re going to scroll down to the D section. You can use the second and then the arrow to go, you know, quicker. Screen by screen. But there is Double Integral right there. And we’re going to enter our function and we’re going to press Alpha first before you enter anything into these entry lines, here. Alpha X times Y plus X squared times Y cubed. I always show you what you’ve entered, you can change it if you want. And now we have to decide whether we want to do it from dy, dx or dx, dy, that’s the order of integration. We’re going to go with number 2, dy, dx. And here we have if dx is on the outside then it’s on the outside here and this is on the inside therefore the ay by is, the limits are involved with the dy inside. So remember that. dx is on the outside therefore these go with the dx. dy is on the inside the limits of integration go from ay to by. So let’s enter those now. And there’s the region. Just like this in notation. So we’re going to do Alpha 1 to Alpha 3. Say it’s okay. We’re going to do Alpha 0 to Alpha 2. I say that’ okay. And there’s out integral right there. We have the function inside here, dy dx. And here’s the x on the outside and the limits of integration 0 to 2 on the inside. So with respect to Y, we integrate with respect to Y. Here’s the answer x squared times y to the fourth over 4 plus x times y squared over 2. And we’re going to do that over the 0 on the 2 limits. So at x equals 2, you add. You see quotation marks here but I can’t, I would like to put parentheses in for those because we’re substituting y equals 2 for all the y’s in this function, here. So you’re going to have to put the parentheses in every time you see quotation marks, put parentheses, okay. And then 4 squared plus 2 x and that’s what that equals and then y equals 0 and then here’s the 0’s in for Y and that equals 0. And 4 x squared plus 2x minus. The upper limit minus the lower limit is 4x squared plus 2 times x. Now we integrate that with respect to the limits 1 and 3 with respect to x. So we integrate that. Here’s the answer here. 4x cubed divided by 3 x squared over 1 in 3. The limits. And x equals 3 here, we’re substituting 3 in for all the x’s equals 45. And x equals 1. You substitute 1 for all the x’s, you get 7/3. So upper minus lower 45 minus 7/3 equals the are is 42.7 square units. Remember the an integral always gives\you the area under a curve. And so I always put square units in there. Alright, have a good one.
Definite Integral with (x,y) Video
Raw Transcript
Hello, Tom of everystepcalculus.com and everystepphysics.com. A definite integral over X and Y. Let’s do it. Index 8 index to get to my menu. Scroll down to D section. Definite Integral X over XY. Double Integral. Enter the function. Alpha before you enter anything into the entry lines. This one on the internet. X times Y squared divided by parentheses, you always put parentheses in denominators. X squared plus one. I don’t know who dreams up these functions but somebody does. Remember, we’re not learning calculus for life long desires unless you’re a math major. We’re learning Calculus to pass a test. To get through Calculus. Never to touch it again. Keep that in mind, okay. Press enter here. And see if that’s what you entered. I say it is. And we’re do it over to DY, DX. And remember that D you integrate with respect to Y first when it’s DY here and DX second. And so DY is these limits of integration. And DX is these limits. So the limits given in this problem were X for 0. Alpha 0, Alpha 1. And for AY was Alpha minus 3. And Alpha 3. And here’s the Integral right here. And we’ve done the integral with respect to Y. Here’s the answer: X times Y cubed divided by 3 times x squared plus 1. And we’re going to do that over -3 and 3. So when Y equals 3, you enter these quotation marks are where you enter parentheses on your paper. Okay. Because that’s substituting Y for anything in these functions, these answers. Another one, -3 is when Y equals minus 3, these is the, you put parentheses around quotations marks. This is the answer. This is the answer for when you put three up there and you subtract the upper limit from the lower. and you get 18 X for x squared. Now we’re doing the integral of that answer over 0 in 1 limits. So we do on the integral of that which equals 9 times log of X squared plus 1. At x equals 1, this is the answer. 9 times log over 2. log 2 and x equals 0. 9 times log over zero x squared plus one which equals zero. Upper limit from the lower is this minus the 0. And so this is the answer also but when you work it out, it comes up to 6.24 square units. Pretty neat, huh? Go to my site and subscribe it you want to see more movies.
Curl Using PQR Notation Example-Video
Raw Transcript
Hello, everyone. Tom from everystepcalculus.com and everystepphysics.com. Curl problem using the PQR System of Notation, for variables. So let’s do it. Index 8 to get to my menu. We’re going to scroll down to Curl. You can hold that button down or you can just press it each time to go down. Here’s P Q R, Curl PQR. We’re going to choose that. Do a Curl problem. Choose PQR again. That’s what you’re doing. That’s how it’s notated. Cartesian up here and vector notation here with the arrows on the ends. We’re going to use these up here. Alpha Y times Z squared. Alpha, you have to press alpha before you enter anything into these entry lines here. Alpha X times Y. Alpha Y squared times Z. I show you what you’ve entered, you can change it if you want. I say it’s okay. This is the tough part do the cross product of partial fractions, here. That’s tough. You gotta remember that and what to do. That’s why I programmed it so you never make a mistake on it. It’s mindless stuff so why ponder it. Put it in a program and use it. Here’s the computations of that. I J K is Cartesian. I is X, J is Y, and K is Z axis. And here’s the answer here. Okay. Now we can do several things but let’s compute it at a point. Number 3. Compute the curl at a point. Let’s enter Alpha 1, Alpha 2, Alpha 3. Again, I show you what you’ve entered in case you made a mistake. It puts the x and the y and the z values into this formula. The quotation marks are there, you should use parentheses where you see quotations. Because your’e substituting 3 for x or Z, in the case Z squared plus 4 times Z times 2 which is Y plus Y. And the answer is 17. Pretty neat, huh? everystepcalculus.com. Goto my site, subscribe to see more videos. Have a good one.
Vectors-Magnitude of A times B
Raw Transcript
Hello, everyone. Tom from everystepcalculus.com and everystepphysics.com. This is an everystepcalculus.com problem. And with my programs. Question on vectors. Let’s get started. Index 8 to get to my menu. Choose A and B vectors. This is a Calculus 3 problem. This student wanted to know how to find the magnitude of A times B. He could get the cross product but he do the magnitude of it. So, let me know you how to do that. You have to enter Alpha before you enter anything into these entry lines, here. So, Alpha minus 2. Alpha one. Alpha one. For the B Vector. Alpha 2, Alpha 1. Alpha 1. So we check see if that’s the vectors that you want. I say it’s okay. A times B is the cross product so we’re going to go to here, A times B. Matrix Multiplication. Write this on your paper, exactly as you see it. There’s the Cartesian System. Notating a vector. Right here. And here’s the answer for the cross product. Zero, four, four. So, we have one vector now which is 0 for X, 4 for Y, and minus four for Z. So now we’re going to go down and we’re gonna find new AB vectors. As we need to put a new vector in for A. So the answer was Alpha zero, Alpha four. That’s for the cross product. Alpha minus four. And we can just quickly go through these because there is no vector for B of A. So now we’re going to go up here and find magnitude of, magnitude of A, number 2. Choose that. This is the way you notate it, it’s got these two lines on the side. It’s called the magnitude of A. Do these calculations. Notice the square root of x square, y squared, z squared and we come up with 5.66 units. Pretty neat, huh? everystepcalculus.com. Have a good one.
Programs Included in Calculus 2 & 3 App
Programs Included in Calculus 2 & 3 App
Raw Transcript
Hello, everyone. This is Tom from everystepcalculus.com and everystepphysics.com. This video is on a menu of Calculus 2 and 3 if you purchased that. What you get. I’m going to go over each item and show you. Index 8 to get to the menu. The busy sign here means that it’s loading the programs. Sometimes it takes longer because of the size of the program but after it’s loaded once, it’s very quick. For instance like this F1 8 to clear, I’m going to press it now. Notice how quickly it comes up right away. I’m going to go up to the top here. And start name the things. Look at this part up here as I name them. A and B vectors, that comes in Calculus 3, generally. You’re doing all sorts of things with adding vectors and subtracting vectors and doing everything possible with them. So A and B vectors, Acceleration, Angle of Vector, Arc Length, that’s the f of x system and then the r t system, Area of a Parallelogram, Component of A Direction of B, Cosine of A and B, that’s the cosine of the A and B vectors. Cross Product, dealing with vectors. Curl computing it at a point, Curl conservative, whether it’s conservative or not, Curl whether it’s divergent, and then the systems of notation which is MNP and PQR for the curl. There’s a double integral, definite integral xy and there’s a definite integral xyz. One is area one is volume. Disk method, Divergence at a point, dot product, double integral, eliminate the parameter, equation of a tangent plane, an equation of a plane, Gradient, Green’s Theorem, Integration by Parts, Interval of Convergence, Line Integral f of xyz, linear approximation 2 variables, linear approximation 3 variables, linear equation, natural log of x the derivative of that, natural log of x the integral, natural log of x solving for x, and then log problems, those are to different bases. Mass and spring of a wire, money, p and q points, parametric equation, partial derivative, partial fractions, partial fraction decomposition, path of objects, polar to rectangle, conversion, position vectors, projection of a on b, projection of b on a, ratio test and series when you’re talking about Taylor and Maclaurin series, rectangular to polar, rectangular box, that’s a standard computation in calculus. Series Convergence, Shell Method, Simpson’s rule, Sine of x cubed, cosine of x squared times. Sketch the graph when you’re talking about p and q points, speed which is the same thing as volume. Sphere center midpoint, Sphere equation, sphere radius, Surface area of Revolution, Surface Integral xy, surface integral xz, surface integral yz. Tangent of log of x, the derivative of that. Natural log of x. Tangent of plane to surface. Taylor and Maclaurin series, Trig and half angled formulas, Trig derivatives and identities, trig integrals, triple integral xyz, triple integral zyx, U Substitution, Unit Tangent Vector, Unit Tangent PQ divided by the magnitude which is PQ. That’s those two lines there on each side of the PQ. Unit Vector Opposite, Vector length, vector between p and q, vector magnitude, Vector, unit, tangent, and Vectors. Which is taking 2 or 3 vectors and finding the angles of those vectors, etc. Quite a series of those. Vector Field Divergent, Velocity, Volume of a parallelpiped, the washer method, and that’s it. Have a good one.
U Substitution Solver-Video
Raw Transcript
Hello, everyone. Tom from everystepcalculus.com and everystepphysics.com. I’m going to do a U Substitution problem. Basically a simple one but nothing is simple in Calculus unless you know what you’re doing. It certainly helps to have a photographic memory. This problem was sent to me by a student. I’m going to do it on the video and show him how to do it and show you how to do it. Index 8 to get to my menu. U Substitution. You’d scroll down to it there. Choose that. We’re going to enter the function. Alpha, left parentheses 6 times x minus 5, close off the parentheses to the 4th power. So here’s what we have. I say it’s okay. So let’s talk a little bit about U Substitution. You should do derivatives in your head within one second. What’s the derivative of this function in here? It’s 6. There’s no x’s nothing, it’s just 6. And you have dx on the outside. Okay. So there’s no x or nothing else on the
outside except dx. So let’s, that’s what you choose for U. So U is 6x minus 5, derivative is 6dx, anytime you see a constant on here. This is the trick that always screwed me up in school. You need to take this out of this side and isolate the dx. Okay, because remember the dx is by itself on the function and now this dx needs to be by itself like here. So you divide both sides by 6 through Algebra. DU divided by 6 equals dx. It variably happens like this. Don’t think it doesn’t. Almost every problem you do on U Substitution, your’e going to take the constant from this side and put it over on this side. Okay. So no U equals 6x minus 5. Therefore, the integral of u to the 4th is the function, u to the 4th times du divided by 6. Now here’s the du we just did, du divided by 6. In integration, the constants always have to come out of the integration. So you have to take one sixth out which I do here. Here’s one sixth out of the integral. And here we have the u to 4 by itself, and the du is by itself. Okay. So now we got one sixth times, and now we do the integral,u to the 5 divided by 5. Okay. So now this constant has to come out of here, too. So we have one sixth times one fifth times u to the 5 plus C. Well one sixth times one fifth is one 30th times 6 and then we substitute back in for u, 6 times x minus 5 to the 5 power plus C. Every U substitution is not in the system and if you learn this system, you’re going to be alive but the main thing is to be able to do derivatives in your head in one second. In your sleep. The derivative of this right here is 6 and you need to look and see if you can match something on the outside, etc. For U substitution. It’s all tricky though until you do it ten thousand times. Calculus is a language and most the cases when I was going to school, it was learning Latin or learning Spanish. I didn’t know what they were talking about. So, have a good one.
Integration by Parts-Question by Student-Video
Raw Transcript
Hello, this is Tom from everystepcalculus.com and everystepphysics.com. A student had a question about E to the X integrals. Integration by parts so let’s do it. Index 8 to get to my menu. We’re going to scroll down here to Integration by Parts. To the I’s, there it is. Waiting for it to load. Whenever you see a busy signal, it’ means it’s loading. Sometimes it will take long but after it loads once, it’s quick. And we’re going to go e to the x problem. Busy again loading another problem. We’re going to enter the function that he was wondering about. Alpha x times yellow key x for the e x and close off the parentheses. I always show you what you’ve entered. You can change it if you want. I say it’s okay. Number 1. Does x equal 1? No, we’re going to choose number 2. That means it’s an integration by part. Otherwise, it’d be a u substitution problem. We’re loading another problem here. Here’s the formula for integration by parts. DV and V is the integral of e to the x. U is x, etc. Here’s the formula. You want to put that all together and write it on your paper. And here’s the answer. X times e to the x plus a minus e to the x. Pretty neat, huh? everystepcalculus.com. Go to my site, subscribe to them so you can see other movies. Have a good one.
Is the Curl Conservative? Video
Raw Transcript
Hello, everyone. This is Tom from everystepcalculus.com. A problem dealing with curl. And whether it’s conservative or not. So let’s do it. Index 8 to get to my menu. Scroll down to curl. They’re all alphabetical. Conservative. And we have the choice of PQR or MNP system. I’m going to use number two MNP system this time. And we’re going to add the function. Alpha before you anything into these entry lines, here. 2 times Y Alpha X squared plus 2 times Y times Z. And Alpha Y squared. I always show you’ve entered so you can change it if you want. I say it’s okay. This is the cross product system for doing to curl. Those are partial derivatives. And we compute each one. This is the I cartesian system. I, J, and K, etc. These turn out to be 00. Let’s see. They’re zeros and this one is not zero. Here’s the answer for the curl. Now go into the menu. Now we want to choose whether it’s conservative. So I’m going to do number one. And so here we have the the calculations and the curl again. Does this equal zero. Say no. Because the curl does not to zero, it is not conservative. So that’s the system. Try to do the curl and try to remember the cross product system of doing those calculations. I never could memorize that that kinda stuff. I have much more important things to memorize. Alright, have a good one.
Curl Using M, N, P Notation-Example-Video
Raw Transcript
Hello, everyone. Tom from everystepcalculus.com and everystepphysics.com. With regard to a curl, there are 2 notating systems. One, PQR and MNP. Why they chose those letters, I have no idea, in math. But that’s the way it is. Some professors use one and some professors use the other. Sometimes they use the Cartesian system which is I, J, and K, also. So I’m going to do an M, N, P system right now. Just throw in arbitrary functions and show you. Index 8 to get to my menu. We’re going to go down here to curls. We’ll go down to M, N, P. I like to, I’m going to just show you the definition of a curl, first. Curl is a vector with a magnitude (length) and direction. It represents the circulation, rotation, twist, or turning force per unit area of a field. Now that’s the best definition I can come up with because I asked that to a lot of times in calculus. I said, what the heck is this, what are you talking about? And even this, I hesitate to believe that it has any value other than some mathematical nonsense that they throw around in calculus to do these problems. A vector field is a three dimensional blob and many small vectors pointing in different directions together forming a pattern of definite form. Curl equals Twist divided by Area. A curl of F (x,y,z) is equal to the, here’s the M N P system and here’s the P Q R system defined within the Cartesian coordinates I J K. And if you’re to use the vector notation, you have these arrows on the side. M, N, P and you have arrows on the P, Q, R system. M, a function (x, y, z) in i direction. N a function (x, y, z) in j direction, and P a function (x,y,z) in k direction. Or used also is P, Q, R, etc. So now let’s do an example. We’re going to choose number 2, MNP. You have to press Alpha before you enter anything into these entry lines, here. Alpha 2 times Y squared times Z. Alpha 5 times X times Y times Z. Now these functions, I’m just dreaming up so. It’s probably going to go off the calculator. The answers. Because the screen is so small. It doesn’t go off the calculator screen on the TI-92 plus but it doesn’t on the Titanium. And then I know that you’re doing homework or experimenting because anytime an equation goes off the, think of it. The rest of your class is scored by partial credit and the class curve. Who else in the class could solve a deep problem in calculus. So will never be on a test because it’s just too hard. You would take too much time. Even if you could solve it, it would take too much time, too much paperwork, there would be no time for the rest of the problems on the test. And I have to program for tests only because of the space of the Titanium for memory use and just sanity. There’s ten million derivations of calculus derivatives and integrals. In each one of these, I have to do on a piece of paper, every one of them, to find the correct step by step process. Once I get done with that, I say it’s the best system for solving a problem but it might not be the system that your professor uses on the blackboard so you want to keep that in mind, too. Here’s the second one for the P. I’m going to put in, let’s put in Y cubed times z squared times X. oh, I didn’t press Alpha first. So we need to go back and change it. So alpha 2 times X squared times Z. Alpha 3 times 5 times X times Y squared. Alpha Z cubed. Now they seem to be correct. I’m going to say okay. Choose number 1. Here’s the matrix system for solving the curl and it’s really a cross product system. I don’t know who can remember this. I can’t, I couldn’t. That’s the reason I programmed it. Why try to memorize something when you can actually program it and have it for the rest of your life? So here’s the answers to what’s going on. With partials with respect to certain other partials. Oh the answer turned out to be not too bad, here. So now we can compute it at a point. Choose number 3. Enter the points, let’s just enter some. Alpha 1, alpha minus 5, alpha 9. Again, I show you what you’ve entered. And you substitute. These would be parentheses on your paper. These quotation marks have to be done in the programming, I can’t do anything different. And it’s substituting 1 for any X or minus 5 for any Y or 9 for any Z in the answer here. Here’s a Y right here, minus 5 but you put parentheses around that because you’re substituting. And the answer turns out to be 377. Pretty neat, huh? Have a good one.
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