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))`.

If f(x) and g(x) are continuous in [0,a] satisfying f(x)=f(a-x) and g(x)+g(a-x)=a then int_(0)^(a)f(x)g(x)dx= a) aint_(0)^(a//2)f(x)dx b) a/2int_(0)^(a)f(x)dx c) -aint_(0)^(a)f(x)dx d)None of these

The value of int _(0) ^(2a) (f (x) dx)/( f (x) + f (2a - x)) is:

If f is real valued function such that f(x+y) = f(x) + f(y) and f(1) = 5 , then find the value of f(100)

If int_(-1)^(4)f(x)dx=4" and "int_(2)^(4)(3-f(x))dx=7 , then find the value of int_(2)^(-1)f(x)dx is

If f is an odd function, then the value of I=int_(-a)^(a)(f(sinx))/(f(cosx)+f(sin^(2)x))dx is