I am confused about how to evaluate an integral. I understand the process, it is only the first step that I need some help on. For example, I'm confused why the integral where a=0 and b=pi/2 sin^5xdx= integral (1-cos^2x)^2sinxdx how do you know how to do this step? Thank you!

Question

amistre64 · Answer

so you are asking how sin^5 = (1-cos^2)^2 * sin  ?

amistre64 · Answer

sin^2+cos^2=1  is a trig identity

subtracting cos^2 from each side gets:  sin^2 = (1-cos^2)

sin^5 = sin^4 * sin

sin^5 = (sin^2)^2 * sin

sin^5 = (1-cos^2)^2 * sin

it all trig identities that you should have learned before calculus

anonymous · Answer

I just realized how easy of a question this was! Thank you!

amistre64 · Answer

youre welcome, good luck