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

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

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

int_(0)^( pi)sin 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)^(2pi) (sin 2 theta)/(a-b cos 2 theta )d theta =

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

Evaluate the following : int_(0)^((pi)/(2)) sin^(3) theta cos^(5) theta d theta