Question
what is the indefinite integral of the function:
f(x)=sin^2 (1/8 * x)
in stages if possible
thanks
f(x)=sin^2 (1/8 * x)
in stages if possible
thanks
Answers
drwls
Let x/8 = u
dx = 8 du
So you want the integral of
8*sin^2 u du
sin^2 u = (1/2)[1 - cos(2u)]
=> integral of 4[1 - cos(2u)] du
Let w = 2u; du = dw/2
= 4u - 2 sin(w)
= x/2 - 2 sin(2u) = x/2 - 2sin(x/4)
Check my thinking. I tend to be sloppy
dx = 8 du
So you want the integral of
8*sin^2 u du
sin^2 u = (1/2)[1 - cos(2u)]
=> integral of 4[1 - cos(2u)] du
Let w = 2u; du = dw/2
= 4u - 2 sin(w)
= x/2 - 2 sin(2u) = x/2 - 2sin(x/4)
Check my thinking. I tend to be sloppy