If `f(x)` is a function satisfying `f(x+a)+f(x)=0` for all `x in R` and positive constant `a` such that `int_b^(c+b)f(x)dx` is independent of `b ,` then find the least positive value of `c`

If f(x) is a function satisfying f(1/x)+x^2f(x)=0 for all nonzero x , then evaluate int_(sintheta)^(cos e ctheta)f(x)dx

The function f satisfying (f(b)-f(a))/(b-a)nef'(x) for any "x"in(a,b) is

If f(x)=f(a+x) , then prove that the value of int_(a)^(a+t) f(x)dx is independent of a.

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 Least positive value fo c if c,k,b are n A.P. is

If f(x)= f(a+x) then prove that the value of overset(a+t)underset(a)int f(x)dx is independent of a.

A continuous real function f satisfies f(2x)=3f(x)AAx in RdotIfint_0^1f(x)dx=1, then find the value of int_1^2f(x)dx

If f'(x)=f(x)+ int_(0)^(1)f(x)dx , given f(0)=1 , then find the value of f(log_(e)2) is

Let f(x)be a function satisfying f(x)=f(x) with f(0)=1 and 'g' be the function satisfying f(x)=g(x)=x^2 the value of the integral int_0^1f(x)g(x)dx is

If f: R->R is a function satisfying f(x+y)=f(x y) for all x ,y in R and f(3/4)=3/4 , then f(9/(16)) is a. 3/4 b. 9/(16) c. (sqrt(3))/2 d. 0

If a continuous function f on [0, a] satisfies f(x)f(a-x)=1, a >0, then find the value of int_0^a(dx)/(1+f(x))