`int_0^a[f(x)+f(-x)]dx=` (A) `0` (B) `2int_0^a f(x)dx` (C) `int_-a^a f(x)dx` (D) none of these

int_(0)^(a)[f(x)+f(a-x)]dx=

int_0^a f(a-x) dx=

int_(0)^(2a)f(x)dx-int_(0)^(a)f(x)dx=

int_(0)^(2a)f(x)dx-int_(0)^(a)f(x)dx=

Let f(x)=f(a-x) and g(x)+g(a-x)=4 then int_0^af(x)g(x)dx is equal to (A) 2int_0^af(x)dx (B) int_0^af(x)dx (C) 4int_0^af(x)dx (D) 0

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

If int_(0)^(2a) f(x)dx=int_(0)^(2a) f(x)dx , then

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

int _(0) ^(2a) f (x) dx = int _(0) ^(a) f (x) dx + int _(0)^(a) f (2a -x ) dx

int_(0)^(a) (f(a+x) + f(a-x) ) dx =