Need help evalulating and integral using symmetry

[John45]

Okay so

[-Pi/2 , Pi/2] (cos2X +cosXsinX -3sinX^5)

so it got the anti derivatives of the first two terms

cos2X = .5sin(X)
cosXsinX = -.5sin^2 (X)
but i have no idea how to get the integral of -3sinX^5

anyways my final answer was 0 because I assumed that -3sinX^5 would be evaluated to 0

any help on answering this would be greatly appreciated

 

[tkhunny]

Why do you seek antiderivatives when you already know you should be using symmetry?

f(x) = sin(x) is an odd function. Your Domain is symmetric about the origin. That piece is zero (0). Why waste any time messing with it?

g(x) = cos(x)sin(x) = (1/2)sin(2x) -- Whoops! Another odd function. Done.