Transcript

Hello, Tom from everystepcalculus.com and  everystepphysics.com. We’re gonna do a problem in calculus regarding integration by parts. Okay, I’m gonna do a series of these because that’s what I’m working on right now or cleaning it up whatever. Answering more problems for people this is once answer was given by a student for Yahoo, integrate Y equals X times E to the 2X. How do I do this does E stay the same I mean these are common questions are you gonna integrate that okay. Well, because it’s E to the X you know that you know you have to learn something in calculus you’re gonna say that’s integration by parts anytime you’re this called a transcendental functioning. So, you have to integrate that with the integration by parts you know so, I’m gonna show you how to do that index 8 to get to my menu. I’m already adding integrate by parts I’ll pull it up here so you can see it integrate by parts. Okay, so that’s what you choose and we’re gonna press enter and we’re gonna choose E to the X here okay. You’re going to scroll to that I’m going to scroll up to that you can press the number in front of it if you want I mean that’s quicker. I’ll do that I’m going to press number two we’re going to integrate some form of E to the X there is E to the X okay.

Now, I’ve already entered the problem here so for quickness and so the simulator doesn’t screw up on me but I’m gonna show you I’m gonna press number two here and go back for you to do it you press alpha first before you enter anything in here. Alpha you’d go X and then X and then this yellow button here and then the X which is the E portion of it. E to the two times X and close off the parenthesis on the right and here’s what you’d have right here okay and we’re gonna say it’s one okay. So, here’s what we do here’s the problem we go U equals x which is out here, D U is equal to a derivative of that which is 1DX okay and then DV is E to the 2X and we’re trying to get the V answer. Which is the integral of the DV with respect to X which turns out to be E to the 2x divided by 2 okay. Write this on your paper just exactly like this okay, the formula for that for integration by parts is UV minus the integral of VDU and so we’re going to add what we just found here. U is X ok times V which is E to the 2x divided by 2 minus the integral of E to the 2x my divided by 2 times the derivative of that which is D U which is 1DX okay and then we clean it up I multiply it together clean up this and here’s what we end up there okay.

So, now we’re gonna do this integral here and when we do the integral it becomes minus E to the 2x divided by 4 plus C. Anytime you do an integration it’s got plus C unless it’s a definite integral where you have a certain range to it and so then where’d we have to distribute the minus sign here. Which I do so it’s plus a minus E to the 2x divided by four now the trick here factor out E to the 2x, if we factor out E to the 2x we get 2x minus 1 times e to the 2x divided by 4 plus C. Which is the answer pretty neat huh go to my site buy my programs and enjoy passing calculus they’re only 40 bucks, well worth the money you’ll have it for the rest of your life in your calculator. You can do calculus like I can do it for the rest of your life where you couldn’t no matter how many books you have in your bookshelf or notes from your professor remember these are null notes from me. In other words once I do a problem and figure out how the step by steps go these are my notes. This is my notes and so you can bring this into any test and you’re gonna pass that test with calculus okay. So. think about that no big deal. Hey, go to my site buy my program and pass calculus. Have a good one.

Raw Transcript

Hello, Tom from everystepcalculus.com and everystepphysics.com. This is a problem from a student regarding Transcendental Integrations. And it involves sin. So, I’m going to show you how my programs do that. Index eight to get to the menu, main menu. I’m already scrolled to integration by parts. Generally they give you that in the problem, in a test or. I’m gonna choose sin here because that’s what the problem is. You can see the problem on your screen. And we enter the problem, here. We have to press alpha before you enter anything in these entry lines in my programs Alpha X times second sin 2 times x. I always show you what you’ve entered, you can change it if you want. Just a little bit
of teaching which I don’t really do in my programs. I show rather than teach. Professors teach and then test on mechanics. I like to show the mechanics because that’s what I needed to pass my classes. So, why is this different? Why is this integration by parts and not U Substitution? Okay well get used to memorizing the derivative of anything inside of function Right away. For instance, like this sin of 2 X here is the derivative of that is 2 times the cosine of 2 x divided, oh no it’s not divided by it’s just a it’s just a 2 times the cosine of x. Well you notice there’s no X there, okay. There has to be an x because it has to match in U Substitution. This x and this DX here. Okay. So all we get here would be 2 DX
and so there’s no X involved in the derivative of this here. Therefore you can’t use U Substitution. So it’s integration by parts which is a different formula so I’m going to keep going and I’ll show. say it’s okay. Integration by parts, you come up DV which is the already the derivative of the sin of 2x and then you’re going to integrate that to get
minus cosine of 2x divided by 2, okay. And then U is equal to X and DU, the derivative of that is 1 DX. So now we do in the formula. vu minus the integral vdu dx, etc. Write all this entire paper exactly as you see it. And you’ll get a hundred percent here’s exactly this step by steps. And the answer is here. Careful now because like for instance minus x cosine of 2x divided by 2, a lot the calculator will come up with line here and do the denominator
by 2 you know and this will have the a line and the denominator is 4. So be hip to that when you’re looking at that because this is exactly the problem. Correct, right here. Alright, have a good one.

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.

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.

e^(2x) Integration by Parts on the TI-89 Series

Raw Transcript

This is a video on integration by parts and doing a integral of e to the x. Some function with e to the x. Get started here, again 2nd alpha so that you can enter the letters of my code to get into my menu index 8( ). Closed parentheses tell the calculator that you want to do a program. You can scroll down to e^(x) integrate, that involves integration by parts. In this program you have In(x) , e^x, sin(x), cos (x) but choose e^(x).
Here is the formula: Evaluate a e^(x)
Integral
=v*u – ∫[v*(du)]dx
Here is an example: 2x*e^(-x) that you can add. So you would know how to put the function in or what function to use or something in that form. It will be on your test, and remember these come from tests so the test that I’ve seen I can do them, the program can do it. It is a certainly difficult subject if you ask me. I’ve programmed it for days and I couldn’t do a problem right now from memory without the help of my calculator. So any time you get a pause, you press enter and go to the next section. You press alpha x* press the blue key and e^ over the x button. You get this system of adding the e to the x like the calculator wants. Add x and closed parentheses. X*e^(x)
And here’s what you’ve entered: ∫[x*e^x]dx that’s for integration.
You can change it if you want otherwise select ok. This will come up
∫[x*e^x]dx
dv= (e^x)dx
v= ∫[e^x]dx
= e^x
u= x
du = (1)dx
You have to choose dv first as dv is the derivative. So we have to integrate that to get up to e. Then we have to get u and the derivative of u. There is a 1 in front of the u, so the derivative of u is 1. In case there was 3x, there would be a 3 there example, du = (3)dx.

Here’s the formula again, here’s what we tried to integrate
∫[x*e^x]dx
= v*u – ∫[v*(du)]dx
= (e^x) [x]
• ∫[(e^x) (1)]dx
= x*e^x
-∫[(e^x)]dx
So then we’re gonna evaluate and here’s the answer
∫[(x*e^x)]dx
= x*e^x
-e^x+c
Remember in tests you’re tested on curves and you get partial credit for anything, if you could put the formula down or anything intelligent you’re gonna get some credit for it. So that’s what my theory was when I was into tests and calculus and to somehow pass the class.
So enjoy my programs, everystepcalculus.com

Raw Transcript