Question

need help with a integral (sin^2(t)cos^4(t)),
I can split it up into:
((1-cos(2t))/2)((1+cos(2t))/2)^2,
but the solution then takes out the constants and make it so its 1/8 infront of the integral, how do you get 1/8? I can get 1/4 but not 1/8

Answer 1

The way I would do it is to apply\[\sin^2t=1-\cos^2t\]them use the double angle formula\[\cos^2t=\frac12(1+\cos(2t))\]

Answer 2

you wanted to know how we get 1/8 ?
[(1-...)/2 ] [(1+...)/2]^2 = [1/2-.....] [1/4+ ...] = [1/8 +....]