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)))=` (A) `a` (B) `a/2` (C) `1/2f(a)` (D) none of these

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

If f(x) and g(x) be continuous functions in [0,a] such that f(x)=f(a-x),g(x)+g(a-x)=2 and int_0^a f(x)dx=k , then int_0^a f(x)g(x)dx= (A) 0 (B) k (C) 2k (D) none of these

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 continuous function in R such that f(x)+f(y)=f(x+y) , then int_-2^2 f(x)dx= (A) 2int_0^2 f(x)dx (B) 0 (C) 2f(2) (D) none of these

Let f(x) be a continuous function in R such that f(x)+f(y)=f(x+y) , then int_-2^2 f(x)dx= (A) 2int_0^2 f(x)dx (B) 0 (C) 2f(2) (D) none of these

Let f (x) be a conitnuous function defined on [0,a] such that f(a-x)=f(x)"for all" x in [ 0,a] . If int_(0)^(a//2) f(x) dx=alpha, then int _(0)^(a) f(x) dx is equal to

Let f (x) be a conitnuous function defined on [0,a] such that f(a-x)=f(x)"for all" x in [ 0,a] . If int_(0)^(a//2) f(x) dx=alpha, then int _(0)^(a) f(x) dx is equal to