`int_(0)^( pi/2)(sin^(2)xdx)/(sin x+cos x)=`

"int_(0)^( pi)x sin^(2)xdx

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

int_(0)^( pi/2)(xdx)/(sin x+cos x)

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

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

int_(0)^( pi/2)e^(x)sin xdx=

int_(0)^(pi//2)x^(3)sin3xdx

int_(0)^( pi/2)sin x*cos^(3)xdx

(i) int_(0)^(pi//2)(sin^(7)x)/((sin^(7)x+cos^(7)x))dx=(pi)/(4) (ii) int_(0)^(pi//2)(sin^(5)xdx)/((sin^(5)x+cos^(5)x))dx=(pi)/(4)

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