Steps to solve this Integral

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MAC-A-TAC

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Jan 9, 2009
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Hello.
I would greatly appreciate any help on the following:
What are the steps to find the integral of this term, where R (radius) is considered a constant?
-½R³(1 - cos² ?)(sin ?) d?

Thank you in advance for your help.
My answer key gives -½R³(-cos ? + ? cos³ ?) + C as the solution.
 
If you are integrating with respect to theta, just factor out all constants and distribute the sin to the 1 and cos^2.

ou'll have two integrals of the form sinu*du and u^2*du.
 
Would I multiply (1- cos² ?) by what is on the outside of the parenthesis, sin ?, which would make it sin ? -sin ? cos² ? ??? :?

Thank you.
 
MAC-A-TAC said:
Would I multiply (1- cos² ?) by what is on the outside of the parenthesis, sin ?, which would make it sin ? -sin ? cos² ? ??? :?

Thank you.
Click to expand...

Yes, that's the idea. Then split into two separate integrals, while leaving all constants outside.
 
The product part (sin ? - sin ? cos² ?) is still giving me problems. As you can see above, the answer has only cos terms. After I intergrate I am still getting the term sin in my answer.:?
Still need help on this one, please.

Thank you.
 
MAC-A-TAC said:
The product part (sin ? - sin ? cos² ?) is still giving me problems. As you can see above, the answer has only cos terms. After I intergrate I am still getting the term sin in my answer.:?
Still need help on this one, please.

Thank you.
Click to expand...

When you integrate sin? - what do you get?

When you integrate sin? * cos[sup:1nhvlc6w]2[/sup:1nhvlc6w]? - what do you get? (think of substituting u = cos?)
 
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