C4 integration by substitution question

You are missing something really important in the question. You can substitute sin(t) but not sin(2t) with u.

From Solomon C integrate 12piSin^2 2t Costt dt limites 0 and pi/2, using substitution u=sint.

I got 4 pi, but the markscheme got 32/5 pi, but i dont understand how they got there

New Limits:
t=0, u=0
t=Pi/2 , u=1

u=sintdu/dt=cost
Therefore 1/cost du =dt

12pisin^2(2t)cost dt =
(12pisin^2(2t)cost)/cost=
12pisin^2(2t)
12pi (sin2t)(sin2t)
12pi (2sintcost)(2sintcost)
48pi sin^2(t) cos^2 (t)
48pi sin^2 (t) (1-sin^2 (t))
48pi u^2 (1-u^2)=
48pi u^2 -48pi u^5

Integrate..... = 16pi u^3 - 48/5 u^6

Sub in u values
(u=1) - (u=0)= Just u=1=
80/5 pi -48/5 pi=
32/5 pi
Hope this helped