Problem

Make the given changes in the indicated examples …

Problem 1 Easy Difficulty

Make the given changes in the indicated examples of this section and then solve the given problems.
In Example $1,$ change $\sin ^{3} x \cos x$ to $\cos ^{3} x \sin x$ and then integrate.

Answer

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Calculus 1 / AB

Basic Technical Mathematics with Calculus

Chapter 28

Methods of Integration

Section 1

The General Power Formula

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Video Transcript

in this question we're integrating this expression notice that is with respect to X. There are a couple ways to integrate this. But for this topic we're using substitution method and the integration power rule. For the integration Power rule. If we're integrating U to the power and respect to you, we add one to the power and divide by the new power. Don't forget to put plus C. For indefinitely grow indefinitely grow means there are no lower upper limits over here. So before we do by brute force this integration let's use substitution substitution will allow us to use power rules easily. So let's you'll be equals to cosign X since there are a lot of it. So do you over the X will be minus sign X. So let's bring the dx up. We'll have minus sine X. D X. So Science Ds is over here so we're lacking over minus sign so that's quite easily soft. We put a minus sign here and we put a minus sign to the sine X. I'm just getting up here so you can see more clearly. Course. Thank you. Access over here now we're ready to substitute since you is called Sine X. We will have you killed now this part minus sine X. D X. Is the you okay using power rule now when we integrate you cute we will have you Cute. The power plus one over the new power plus C. So we will hear minus you to power 4/4 plus C. But we cannot leave our answering you because we are actually supposed to integrate respect to X. So our answer has to be an X. So minus now you is called sign X. So you too powerful because sign four X over four plus C. This is our final answer.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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