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

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

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

The integral int_(0)^( pi)f(sin x)dx is equivalent to

Prove the equality int_(0)^(pi) f (sin x) dx = 2 int_(0)^(pi//2) 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 .

If int_(0)^(pi) x f(sinx) dx=A int_(0)^((pi)/(2))f(sinx)dx , then the value of A is -

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

If f:[0,pi]rarr R is continuous and int_(0)^( pi)f(x)sin xdx=int_(0)^( pi)f(x)cos xdx=0 then the number of roots of f(x) in (0,pi) is ...

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

If A=int_(0)^( pi)(sin x)/(x^(2))dx, then int_(0)^((pi)/(2))(cos(2x))/(x)dx, is equal to: