Calculus AB Question. Please Help ive been tyring all day

TheMathProf
Sun, 01 Mar 2009 19:20:03 +0000

Rewrite [cos(w)]^2 as 1 - [sin(w)]^2. Then:


integral([cos(w)]^3 dw)
= integral(cos(w)[1 - (sin(w))^2] dw)
= integral([cos(w) - cos(w)[sin(w)]^2] dw).

The first term of the integral is straightforward, and the second term of the integral can be solved using u-substitution with u = sin w.

That being said questions like #3 that require trig identities to rewrite them are not on the AP Exam, even if they later turn into u-substitution questions.