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

Prove that int_-2^2 f(x^4)dx=2int_0^2 f(x^4)dx

Let f(x) be an integrable odd 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

Let f(x)=max. {2-x,2,1+x} then int_(-1)^1 f(x)dx= (A) 0 (B) 2 (C) 9/2 (D) none of these

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 differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(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

Property 8: If f(x) is a continuous function defined on [-a; a] then int_(-a) ^a f(x) dx = int_0 ^a {f(x) + f(-x)} dx

Let f be a differentiable function such that f'(x) = f(x) + int_(0)^(2) f(x) dx and f(0) = (4-e^(2))/(3) . Find f(x) .