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

(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 .

Show that, int_(0)^(pi)xf(sinx)dx=(pi)/(2)int_(0)^(pi)f(sinx)dx .

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

Which of the following are true ?(i)int_(a)^( pi-a)xf(sin x)dx=(pi)/(2)int_(a)^( pi-a)f(sin x)dx( ii) int_(-a)^(a)f(x^(2))dx=2int_(0)^(a)f(x^(2))dx( iii) int_(0)^(n pi)f(cos^(2)x)dx=n int_(0)^( pi)f(cos x)dx,n in N (iv) int_(0)^(b-c)f(x+c)dx=int_(c)^(b)f(x)dx

Show that int_(0)^(pi)xf(sinx)dx=(pi)/2 int_(0)^(pi)"fr"(sinx)dx .

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

underset is If int_(0)^( pi)xf(sin x)dx=A int_(0)^((pi)/(2))f(sin x)dx, then A

STATEMENT 1:int_(0)^( pi)x sin x cos^(2)xdx=(pi)/(2)int_(0)^( pi)sin x cos^(2)xdxint_(b)^(b)xf(x)dx=(a+b)/(2)int_(a)^(b)f(x)dx