If `int_a^b(f(x)-3x)dx=a^2-b^2` then the value of `f(pi/6)` is ___

If overset(b)underset(a)int {f(x)-3x}dx=a^(2)-b^(2) , then the value of f((pi)/(6)) , is

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

Suppose f is continuous on [a,b] & f(a)=f(b)=0 & int_(a)^(b)f^(2)(x)dx=1 then the minimum value of int_(a)^(0)(f^(')(x))^(2)dx int_(a)^(b) x^(2)f^(2)(x)dx is k , then 8k is

If int_(-3)^(2)f(x) dx= 7/3 and int_(-3)^(9) f(x) dx = -5/6 , then what is the value of int_(2)^(9)f(x) dx ?

IF int_(-3)^2 f(x) dx=7/3 and int_(-3)^9 f(x) dx=-5/6 then what is the value of int_(2)^(9)f(x) dx

Prove that int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx and hence evaluate int_((pi)/(6))^((pi)/(3))(1)/(1+sqrt(tanx))dx.

If f(x)=x+sinx , then find the value of int_pi^(2pi)f^(-1)(x)dx .

If f(x)=x+sinx , then find the value of int_pi^(2pi)f^(-1)(x)dx .