If `U_(n)=int_(0)^(pi)(1-cosnx)/(1-cosx)dx` where `n` is positive integer of zero, then
The value of `int_(0)^(pi//2)(sin^(2)n theta)/(sin^(2) theta) d theta` is

If U_(n)=int_(0)^(pi)(1-cosnx)/(1-cosx)dx where n is positive integer of zero, then The value of U_(n) is

Evaluate int_(0)^(pi)x^(2) cosnxdx, where n is positive integer.

Evaluate int_(0)^(pi//2)(costheta)/((1+sintheta)(2+sintheta))d theta

If U_n=int_0^pi(1-cosnx)/(1-cosx)dx , where n is positive integer or zero, then show that U_(n+2)+U_n=2U_(n+1)dot Hence, deduce that int_0^(pi/2)(sin^2ntheta)/(sin^2theta)=1/2npidot

Evaluate: int_(0)^(pi//2) sqrtsinthetacos^(5)theta d theta

Evaluate: int_(0)^(2pi)x^(2) sinnxdx, where n is positive integer.

Evaluate: int_(0)^(pi/2)(costheta)/((1+sintheta)(2+sintheta))d theta .

The value of I=int_(0)^(pi)x(sin^(2)(sinx)+cos^(2)(cosx))dx is