If a continuous function `f` on `[0, a]s a t i sfi e sf(x)f(a-x)=1, a >0,` then find the value of `int_0^a(dx)/(1+f(x))`

If a continuous function f on [0,a] satisfies f(x)f(a-x)=1,agt0 , then find the value of int_(0)^(a)(dx)/(1+f(x)) .

f(0)=1 , f(2)=e^2 , f'(x)=f'(2-x) , then find the value of int_0^(2)f(x)dx

Let f(x) be a continuous function on [0,4] satisfying f(x)f(4-x)=1. The value of the definite integral int_(0)^(4)(1)/(1+f(x))dx equals -

If f(x) is a continuous function in [0,pi] such that f(0)=f(x)=0, then the value of int_(0)^(pi//2) {f(2x)-f''(2x)}sin x cos x dx is equal to

If fandg are continuous function on [0,a] satisfying f(x)=f(a-x)andg(x)+g(a-x)=2 then show that int_(0)^(a)f(x)g(x)dx=int_(0)^(a)f(x)dx

If f and g are continuous functions on [0,a] such that f(x)=f(a-x) and g(x)+g(a-x)=2 then show that int_(0)^(a)f(x)g(x)dx=int_(0)^(a)f(x)dx

If f:RrarrR defined by f(x)=sinx+x , then find the value of int_0^pi(f^-1(x))dx

A continuous real function f satisfies f(2x)=3(f(x)AA x in R. If int_(0)^(1)f(x)dx=1 then find the value of int_(1)^(2)f(x)dx