`int_(0)^( pi/4)sin^(4)x*dx`

int_(0)^(pi//4)sin^(2)x dx=

int_(0)^( pi/4)sin|x|dx

int_(0)^( pi)sin^(3)x*dx=(4)/(3)

int_(0)^(pi/4) sin^(3) x dx=(2)/(3)

int_(0)^( pi/2)(sin^(4)x)/(sin^(4)x+cos^(4)x)dx

int_(0)^(pi) x sin^(4) x dx is equal to

" (8) "int_(0)^( pi)sin x*cos^(4)x*dx

int_(0)^(pi//2) sin ^(4) x dx

int_(0)^(pi//4) sin ^(2) x dx

(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)