Question

Integrate 144(sin(theta)^2)^(3/2).

Answer 1

\[144(\sin^2(\theta))^{\frac{3}{2}}=144\sin^3 \theta=144\sin \theta (\sin^2 \theta)\]\[=144\sin\theta(1-\cos^2\theta)\]
do a u substitution for cos, and done.

Answer 2

Thank you. I had it done that way but thought it was wrong. Substituting cos for u should cancel out the sin since du would equal sin correct?

Answer 3

correct :)

Answer 4

Thanks again. I realized what I did wrong. I did not integrate the 1 in (1-cos).

Answer 5

The integral has the bounds from 0 to 2pi. When I evaluate the integral the answer I get is 0 but it's supposed to be 384. I do not understand how that answer is achieved