Question

How to simplify the (integral from 3cos^2 (theta) d*theta from 0 to pi) to (3*integral of cos^2 (theta) d*theta from 0 to pi/2)?

Answer 1

It doesn't simplify like that, unfortunately. You can, however, write it as
\[\int_0^\pi3\cos^2\theta~d\theta=2\int_0^{\pi/2}3\cos^2\theta~d\theta=6\int_0^{\pi/2}\cos^2\theta~d\theta\]

Answer 2

Thank you. The book must be wrong then.