Archives for 2014
Given Vectors A&B find Projection A on B-Video
Find the gradient of
f(x,y,z)=x^2+y^2-4z, at the point (2,-1,1)
Unit Vector with P & Q Points Q to P
L’hospitals Rule Using Limits to Infinity
Gradient Solver at Point (1,2) Video
L’hospitals Rule & Indeterminate Quotients-Video
Unit Vector With P&Q Points-Video
Length of a Vector Using P&Q Points-Video
Triple Integral dz, dy, dx Solver-Video
Magnitude of a Vector P&Q Points-Video
Equation of a Plane Using 3 Points-Video
Solving Equation of Plane 2 Points-Video
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.
- 1
- 2
- 3
- …
- 5
- Next Page »