Hi the problem is to evaluate the following
integral sign ("S") b=pi/3 a=0 sin^3 x dx
so using the identity 1= sin^2 x + cos^2 x
S sin^3 x dx = S sin x (1-cos^2 x) dx
So if I let u= cos x du = sin x dx
Then the original equation becomes = S (1-u^2) du
= u - (1/3) u^3
Substituting back and now applying a= 0 and b = pi/3
= (cos pi/3 - (1/3) cos^3 pi/3) - (cos 0 - (1/3) cos^3 0)
First am I doing this right?? And second if this is right does cos^3 pi/3 = 1/8?
Thanks
Calculus Beginner