Let `f(x)` be a continuous function such that `int_0^1 f(x) (2x-f(x))dx=1/3` then the value of `f(3)` equals

Let f(x) be a continuous function such that int_(n)^(n+1) f(x) dx=n^(3) , ninZ . Then the value of the integeral int_(-3)^(3) f(x) dx, is

Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in [0,a] . Then, the value of the integral int_(0)^(a) (1)/(1+e^(f(x)))dx is equal to

Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in [0,a] . Then, the value of the integral overset(a)underset(0)int (1)/(1+e^(f(x)))dx is equal to

Let f(x) be a non-negative continuous function defined on R such that f(x)+ f(x+(1)/(2))=3 ,then the value of (1)/(1008)*int_(0)^(2016)f(x)dx

Let f(x) be a non-negative continuous function defined on R such that f(x)+f(x+1/2)=3 , then the value of 1/1008 int_(0) ^(2015) f(x) dx is

let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in[0,a] then int_0^a dx/(1+e^f(x) is equal to

Let f(x) is a continuous function If f(1)=1 and int_(0)^(x)t.f(2x-t)dt=(1)/(2)tan^(-1)(x^(2)) then the value of a? 4int_(1)^(2)f(x)dx is equal to

Let f:R to R be continuous function such that f(x)=f(2x) for all x in R . If f(t)=3, then the value of int_(-1)^(1) f(f(x))dx , is