Calculus help 1 problem?

Question

Fundamental theorem of Calculus:

(pi/4)
∫(1-sin2t)^3cos2tdt
0

Correct Answer 1/8

I'm lost how would I solve this?

Answer 1

Where  1- sin2t = x

 - 2cos(2t) dt = dx

  cos2t dt = - 1/2 dx

Therefore x = 1- sin2t

Apply fundamental therom

Apply limits on both sides

Since sin(π/2) = 1 and sin(0) = 0

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