`int_(-1)^(3/2) |xsinpix|dx=[(-xcospix)/pi+(sinpix)/pi^2]_(-1)^1-[(-xcospix)/pi+(sinpix)/pi^2]_1^(3/2)`

int _ (- 1) ^ ((3) / (2)) | x sin pi x | dx = [(- x cos pi x) / (pi) + (sin pi x) / (pi ^ (2))] _ (- 1) ^ (1) - [(- x cos pi x) / (pi) + (sin pi x) / (pi ^ (2))] _ (1) ^ ((3) / (2) )

int_(-2)^(2)abs(xcospix)dx is equal to

int_(-(pi)/(2))^((pi)/(2))(sin^3xdx)/(1+cosx)= .

If int_(-1)^(3//2)|xsinpix|dx = (k)/(pi^(2)) , then the value of k is :

If int_(-1)^(3//2)|xsinpix|dx = (k)/(pi^(2)) , then the value of k is :

int_(-pi/2)^(pi/2)(1+sin^2x)/(1+pi^(sinx))dx=

int_(pi//4)^(pi//2)(dx)/((1-cos2x))

I_(1)=int_(0)^((pi)/2)(sinx-cosx)/(1+sinxcosx)dx, I_(2)=int_(0)^(2pi)cos^(6)dx , I_(3)=int_(-(pi)/2)^((pi)/2)sin^(3)xdx, I_(4)=int_(0)^(1) In (1/x-1)dx . Then

I_(1)=int_(0)^((pi)/2)(sinx-cosx)/(1+sinxcosx)dx, I_(2)=int_(0)^(2pi)cos^(6)dx , I_(3)=int_(-(pi)/2)^((pi)/2)sin^(3)xdx, I_(4)=int_(0)^(1) In (1/x-1)dx . Then