If `int_0^(pi)(x^3cos^4xsin^2x)/(pi^2-3pix+3x^2)dx=lambdaint_0^(pi/2)sin^2xdx`, then the value of `lambda` is:

If int _(0) ^(x) (x ^(3) cos ^(4) x sin ^(2)x)/(pi^(2) -3pix + 3x ^(2))dx = lamda int _( 0)^(pi//2)sin ^(2) x dx, then the value of lamda is:

int_(0)^(pi//4)sin2xsin3xdx

int_(0)^((pi)/(2))cos^(4)xsin^(3)xdx

int_(0)^( pi/4)sin2x sin3xdx

int_(0)^( pi/4)sin2x*sin3xdx

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

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

int_0^(pi/2) (sin^(3)x)/(cos^(3)x+sin^(3)x) dx =