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

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

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

The value of int_(0)^(pi//2)x|sin^(2)x-(1)/(2)|dx is equal to (api)/(b) where a,b are co-prime numbers, then a.b is ____________

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

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

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

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

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

For n gt 0 int_(0)^(2pi)(x sin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx= ….

int_(0)^(pi) x sin x cos^(2)x\ dx