Suppose `f,f' and f"` are continuous on `[0,e]` and that `f^(prime)(e)=f(e)=f(1)=1 and int_1^e(f(x))/(x^2)dx=1/2,` then the value of `int_1^0 f*(x)ln xdx` equals.

Suppose f, f' and f'' are continuous on [0, e] and that f'(e )= f(e ) = f(1) = 1 and int_(1)^(e )(f(x))/(x^(2))dx=(1)/(2) , then the value of int_(1)^(e ) f''(x)ln xdx equals :

Suppose f, f' and f'' are continuous on [0, e] and that f'(e )= f(e ) = f(1) = 1 and int_(1)^(e )(f(x))/(x^(2))dx=(1)/(2) , then the value of int_(1)^(e ) f''(x)ln xdx equals :

Suppose f, f' and f'' are continuous on [0, e] and that f'(e )= f(e ) = f(1) = 1 and int_(1)^(e )(f(x))/(x^(2))dx=(1)/(2) , then the value of int_(1)^(e ) f''(x)ln xdx equals :

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

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

Suppose that f,f^prime and f prime prime are continuous on [0, ln 2] and that f (0) = 0, f prime(0) = 3, f(In 2) = 6,f prime(ln 2) = 4 and int_0^(ln 2) e^(-2x)*f(x)dx=3. Find the value of int_0^(ln2) e^(-2x)*f prime prime(x)dx.

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

If f(x)=1+1/x int_1^x f(t) dt, then the value of f(e^-1) is

If f(x)=1+1/x int_1^x f(t) dt, then the value of f(e^-1) is

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