Integration by Parts

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.