Let y=f(x) be a differentiable function `AA xin R` and satisfies:
`f(x)=x+int_(0)^(1)x^(2)zf(z)dz+int_(0)^(1)xz^(2)f(z)dz.`

Let f be a differentiable function on R and satisfying the integral equation x int_(0)^(x)f(t)dt-int_(0)^(x)tf(x-t)dt=e^(x)-1 AA x in R . Then f(1) equals to ___

Let f(x) be a differentiable function in the interval (0, 2) then the value of int_(0)^(2)f(x)dx

Let f :R ^(+) to R be a differentiable function with f (1)=3 and satisfying : int _(1) ^(xy) f(t) dt =y int_(1) ^(x) f (t) dt +x int_(1) ^(y) f (t) dt AA x, y in R^(+), then f (e) =

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) 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=

Let f:RtoR be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . y=f(x) is

Let f(x) be a differentiable function satisfying f(x)=int_(0)^(x)e^((2tx-t^(2)))cos(x-t)dt , then find the value of f''(0) .

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) .

Let f be a differentiable function satisfying f(x)+f(y)+f(z)+f(x)f(y)f(z)=14" for all "x,y,z inR Then,

Let f be a differentiable function satisfying int_(0)^(f(x))f^(-1)(t)dt-int_(0)^(x)(cost-f(t)dt=0 and f((pi)/2)=2/(pi) The value of lim_(x to 0)(cosx)/(f(x)) is equal to where [.] denotes greatest integer function