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

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) 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)+f(x)=0 then int_(a)^(x)f(t)dt is

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=

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

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

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

If f(a-x)=f(x) and int_(0)^(a//2)f(x)dx=p , then : int_(0)^(a)f(x)dx=

if f(x) is a differential function such that f(x)=int_(0)^(x)(1+2xf(t))dt&f(1)=e , then Q. int_(0)^(1)f(x)dx=