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Write out your steps to show that the derivative of the function 1/8{32sin(2)+1/4sin(4)} really is the function sin^4(). How could you generalize this method to

Write out your steps to show that the derivative of the function

1/8{32sin(2)+1/4sin(4)} really is the function sin^4().

How could you generalize this method to find antiderivatives for other powers of sin?

Can you now find antiderivatives for products of powers like

sin^k()cos^m()?

Explain carefully, and make sure to be explicit about conditions on k and m for your explanation to make sense.

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