If `int_0^asqrt(x)dx=2aint_0^(pi//2)sin^3xdx` find the value of integral `int_a^(a+1)xdxdot`

If int_(0)^(a)sqrt(x)dx=2a int_(0)^( pi/2)sin^(3)xdx find the value of integral int_(a)^(a+1)xdx

(i)If int_0^asqrtxdx=2aint_0^(pi/2)sin^3xdx ,find the value of a. (ii)Hence find int_a^(a+1)xdx

IF int_0^a sqrtx dx=2a int_0^(pi//2) sin^3 x dx, find int_a^(a+1) x dx .

Find the value of int_0^(pi/2)sin2xdx

Find the value of int_0^(pi/2)sin2xdx

Show that, int_(0)^(pi)sin^(3)xdx=2int_(0)^((pi)/(2))sin^(3)xdx and hence, find the value of int_(0)^(pi)sin^(3)xdx .

Show that, int_(0)^(pi)sin^(4)xdx=2int_(0)^((pi)/(2))sin^(4)xdx , hence, find the value of int_(0)^(pi)sin^(4)xdx .

The value of the integral int_(0)^(pi) | sin 2x| dx is

The value of the integral int_(0)^(pi)(1-|sin 8x|)dx is

(i) Show that int_(0)^(pi)xf(sinx)dx =(pi)/(2)int_(0)^(pi)f (sin x)dx. (ii) Find the value of int_(-1)^(3//2)|x sin pix|dx .