`int cos^4(theta) sin(theta) d theta` Evaluate the indefinite integral.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

You need to use the following substitution  `cos theta = u` , such that:

`cos theta = u=> -sin theta d theta = du =>sin theta d theta = -du`

`int cos^4 theta*sin theta d theta = - int u^4 du`

`- int u^4 du = -(u^5)/5 + c`

Replacing...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

You need to use the following substitution  `cos theta = u` , such that:

`cos theta = u=> -sin theta d theta = du =>sin theta d theta = -du`

`int cos^4 theta*sin theta d theta = - int u^4 du`

`- int u^4 du = -(u^5)/5 + c`

Replacing back   `cos theta` for` u` yields:

`int cos^4 theta*sin theta d theta = -((cos theta)^5)/5 + c`

Hence, evaluating the indefinite integral, yields `int cos^4 theta*sin theta d theta = -((cos theta)^5)/5 + c`

Approved by eNotes Editorial Team