If `a,b>0` and `int_0^ooln(bx)/(x^2+a^2)dx=pi/(2a)` then the value of `(ab)` is

If a,b>0 and int_(0)^(oo)(ln(bx))/(x^(2)+a^(2))dx=(pi)/(2a) then the value of (ab) is

If a,b>0 and int_(0)^(oo)(ln(bx))/(x^(2)+a^(2))dx=(pi)/(2a) then the value of (ab) is

If int _(a)^(b) x^(3) dx = 0 and if int _(a)^(b) x^(2) dx = 2/3 , then the values of a and b respectively are

If the value of int_0^pi(x/(1+sinx))^2dx=lambda , then find the value of the integral =int_0^pi[(2x^2*cos^2(x/2))/(1+sinx)^2]dx

int_0^(pi//2) x^2 cos 2x dx

If int_(0)^(pi)((x)/(1+sinx))^(2) dx=A, then the value for int_(0)^(pi)(2x^(2). cos^(2)x//2)/((1+ sin x^(2)))dx is equal to

IF f(x)=A si n ((pi x)/2)+B and f'(1/2)=sqrt2 and int_0^1 f(x)dx =(2A)/pi then what is the value of B

Given that int_0^oo(x^2)/((x^2+a^2)(x^2+b^2)(x^2+c^2))dx=pi/(2(a+b)(b+c)(c+a)) the value of int_0^oo(dx)/((x ^2+4)(x^2+9)), is pi/(60) b. pi/(40) c. pi/(20) d. pi/(80)

int_0^pi (cos^2x)dx ,