int_(0)^((3)/(2))|x sin pi x|dx

Evaluate: int_0^(3//2) |x sin pi 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 .

int_(0)^(1)(tan^(-1)x)/(x)dx is equals to int_(0)^((pi)/(2))(sin x)/(x)dx(b)int_(0)^((pi)/(2))(x)/(sin x)dx(1)/(2)int_(0)^((pi)/(2))(sin x)/(x)dx(d)(1)/(2)int_(0)^((pi)/(2))(x)/(sin x)dx

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

If A=int_((rho)/(2))^((pi)/(2))cos(sin x)dxB=int_(0)^((pi)/(2))sin(cos x)dx and C=int_(0)^((pi)/(2))cos(x)dx

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

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

int_ (0) ^ ((pi) / (2)) (sin x) / (sin x + cos x) dx = int_ (0) ^ ((pi) / (2)) (cos x) / (sin x + cos x) dx = int_ (0) ^ ((pi) / (2)) (dx) / (1 + cot x) = int_ (0) ^ ((pi) / (2)) (dx) / ( 1 + time x) = (pi) / (4)

Show : int_(0)^((pi)/(2))sinxf(sin2x)dx=int_(0)^((pi)/(2))cosxf(sin2x)dx