If `f^(prime)(x)=f(x)+int_0^1f(x)dx ,gi v e nf(0)=1,` then the value of `f((log)_2 2)` is (a)`1/(3+e)` (b) `(5-e)/(3-e)` (c)`(2+e)/(e-2)` (d) none of these

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

If int((x-1)/(x^(2)))e^(x)dx=f(x)e^(x)+c, then write the value of f(x)

If int((x-1)/(x^(2)))e^(x)dx=f(x)e^(x)+C, then write the value of f(x)

"If " f(x)=int(dx)/(x^(1//3)+2) " and "f(0)=12log_(e)2, " then the value of " f(-1) " is"-.

Suppose f is a differentiable real function such that f(x)+f^(prime)(x)lt=1 for all x , and f(0)=0, then the largest possible value of f(1) is (1) e^(-2) (2) e^(-1) (3) 1-e^(-1) (4) 1-e^(-2)

f(0)=1 , f(2)=e^2 , f'(x)=f'(2-x) , then find the value of int_0^(2)f(x)dx

The value of int_(1)^(e)((tan^(-1)x)/(x)+(log x)/(1+x^(2)))dx is tan e(b)tan^(-1)e tan^(-1)((1)/(e))(d) none of these

If f(0)=f(1)=0,f'(1)=2 and y=f(e^(x))e^(f(x)), write the value of (dy)/(dx) at x=0

If 2f(x)+f(-x)=(1)/(x)sin(x-(1)/(x)) then the value of int_((1)/(e))^(e)f(x)dx is