Question

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!

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

youre welcome, good luck