Let f be an odd continous function which is periodic with priod 2 if g(x) = `int_0^x f(t)` dt then

Let f(x) = int_2^x f(t^2-3t+2) dt then

Let f : R rarr R be a continuous function which satisfies f(x) = int_0^x f(t) dt . Then the value of f(log_e 5) is

Let f:RtoR be a continuous function which satisfies f(x)=int_(0)^(x)f(t)dt . Then the value of f(log_(e)5) is

If f(x)=int_0^x(sint)/t dt ,x >0, then

Let f(x) be a continuous periodic function with period T. Let I= int_(a)^(a+T) f(x)dx . Then

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 T le0 be a fixed real number suppose f is continuous function such that for all x in R f(x+T)=F(x) if I=int_0^T f(x)dx then the value of int_3^(3+3T)f(2x)dx is

Let f(x), xge0 , be a non-negative continous function,and let F(x) = int_(0)^(x)f(t)dt, xge0 , if for some cgt0,f(x)lec F(x) for all xge0 , then show that f(x)=0 for all xge0 .

If f(x) = is an odd periodic function with period 2, then f(4) equals

Let f(x) and phi(x) are two continuous function on R satisfying phi(x)=int_(a)^(x)f(t)dt, a!=0 and another continuous function g(x) satisfying g(x+alpha)+g(x)=0AA x epsilonR, alpha gt0 , and int_(b)^(2k)g(t)dt is independent of b If f(x) is an odd function, then