int_(-pi)^((pi)/(2))sin^(2)xdx=

Show that int_(0)^((pi)/(2))sin^(2)xdx=int_(0)^((pi)/(2))cos^(2)xdx=pi/4 .

Prove that int_(0)^((pi)/(2))sin^(2)xdx=int_(0)^((pi)/(2))cos^(2)xdx=(pi)/(4)

int_(0)^((pi)/(2))sin^(2)xdx

int_(0)^((pi)/(2))sin^(3)xdx

By using the properties of definite integrals, evaluate the integrals int_((-pi)/2)^(pi/2)sin^(2)xdx

By using the properties of definite integrals, evaluate the integrals int_((-pi)/2)^(pi/2)sin^(2)xdx

Show that int_(-pi//2)^(pi//2)sin^(7)xdx=0 .

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