Let `f(x)` be a differentiable function on `R` such that `f'(5-x)=` `f'(x)AA x in[0,5]` with `f(0)=-10&` `f(5)=50`,then the value of `5int_(0)^(5)f(x)dx`

f:[0,5]rarrR,y=f(x) such that f''(x)=f''(5-x)AAx in [0,5] f'(0)=1 and f'(5)=7 , then the value of int_(1)^(4)f'(x)dx 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=

Let f(x) is a differentiable function on x in R , such that f(x+y)=f(x)f(y) for all x, y in R where f(0) ne 0 . If f(5)=10, f'(0)=0 , then the value of f'(5) is equal to

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let f(x) be a differentiable function satisfying f(y)f(x/y)=f(x) AA , x,y in R, y!=0 and f(1)!=0 , f'(1)=3 then

If f(x) is a differentiable function satisfying |f'(x)|le4AA x in [0, 4] and f(0)=0 , then

Let f(x) be a continuous function such that f(0) = 1 and f(x)=f(x/7)=x/7 AA x in R, then f(42) is

Let f be a differentiable function defined for all x in R such that f(x^(3))=x^(5) fol all x in R,xne0 . Then the value of f'(8) , is

Let f(x) be a real valued function such that f(x)=f(121/x), AA x>0 .If int_1^11 f(x)/xdx=5 , then the value of int_1^121f(x)/xdx is equal to

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) .