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 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 an integrable old function in [-5,5] such that f(10+x)=f(x) , then int_x^(10+x) f(t)dt= (A) 0 (B) 2int_0^5 f(x)dx (C) gt0 (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)))= (A) a (B) a/2 (C) 1/2f(a) (D) none of these

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

Property 7: Let f(x) be a continuous function of x defined on [0;a] such that f(a-x)=f(x) then int_(0)^(a)xf(x)dx=(a)/(2)int_(0)^(a)f(x)dx

If f(x) is a continuous function such that f(x)|0,AA x in[2,10] and int_(4)^(8)f(x)dx=0 then find

If f is an integrable function such that f(2a-x)=f(x), then prove that int_0^(2a)f(x)dx=2int_0^af(x)dx

Let f(x) be a continuous function in R such that f(x) does not vanish for all x in R . If int_1^5 f(x)dx=int_-1^5 f(x)dx , then in R, f(x) is (A) an even function (B) an odd function (C) a periodic function with period 5 (D) none of these

if f(x)=|x-1| then int_(0)^(2)f(x)dx is

A continous function f(x) is such that f(3x)=2f(x), AA x in R . If int_(0)^(1)f(x)dx=1, then int_(1)^(3)f(x)dx is equal to