`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_(2-a)^(2+a)f(x)dx is equal to [where f(2-alpha)=f(2+alpha) AAalpha in R (a) 2 int_2^(2+a)f(x)dx (b) 2int_0^af(x)dx (c) 2int_2^2f(x)dx (d) none of these

int_(2-a)^(2+a)f(x)dx is equal to [where f(2-alpha)=f(2+alpha) AAalpha in R (a) 2 int_2^(2+a)f(x)dx (b) 2int_0^af(x)dx (c) 2int_2^2f(x)dx (d) none of these

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 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 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

Which of the following is incorrect? int_(a+ c)^(b+c)f(x)dx=int_a^bf(x+c)dx int_(ac)^(b c)f(x)dx=cint_a^bf(c x)dx int_(-a)^af(x)dx=1/2int_(-a)^a(f(x)+f(-x)dx None of these

int_(m)^(0)f(x)dx is

If int_0^af(2a-x)dx=m and int_0^af(x)dx=n, then int_0^(2a) f(x) dx is equal to

int e^x {f(x)-f'(x)}dx= phi(x) , then int e^x f(x) dx is

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