int_(0)^( pi/2)theta sin theta cos theta d theta

int_0^(2pi) theta sin^2 theta cos theta d theta is equal to :

int_(0)^( pi/2) sin^(2)theta cos theta d theta

int _(0) ^(pi) sin ^(2) theta cos theta d theta

If I_(1)=int_(0)^(1)(dx)/(e^(x)(1+x)) and I_(2)=int_(0)^( pi/2)(e^(sin^(2)theta)sin theta cos theta d theta)/((2-sin^(2)theta)) then (where [ .] denotes greatest integer function)

int_(0)^( pi)sin theta d theta =

Evaluate int_(-pi//2)^(pi//2) ( sin theta cos theta) d theta .

Let the be an integrable function defined on [0,a] if I_(1)=int_(pi//2)^(pi//2) cos theta f(sin theta cos ^(2) theta)d theta and I_(2)=int_(0)^(pi//2)sin 2 theta f(sin theta cos ^(2) theta)d theta then