`int_(0)^( pi)x(1-x)dx`

int_(0)^( pi)(x)/((1+x)(1+x^(2)))dx

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

If int_(0)^( pi)f(x)dx=pi+int_(pi)^(1)f(t)dx, then the value of (L) is :

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

(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)^( pi/2)(x)/((1-x^(2)))dx

int_(0)^( pi)(x sin(x))/(1+sin(x))dx

Prove that: int_(0)^( pi)(x)/(1-cos alpha sin x)dx=(pi(pi-alpha))/(sin alpha)

Evaluate the following definite integrals: int_(0)^(pi//2)(1-sinx)/(x+cos x)dx

[-int_(0)^(1)sqrt(1-x)dx],[=(pi)/(2)-1]