How to Evaluate the Integral of a Derivative at a Given Point

[Samuelb88]

Evaluate the integral... ?:(

Homework Statement

Suppose that the function f and g and their derivatives have the following values at x=0, x=1.

$$f(0)=1, f(1)=3$$
$$f'(0)=5, f'(1)=\frac{1}{3}\right)$$
$$g(0)=1, g(1)=-4$$
$$g'(0)=\frac{1}{3}\right),g'(1)=-\frac{8}{3}\right)$$

Evaluate the integral:

$$\frac{d}{dx}\right)(f^(^3^)(x^1^/^2))|$$ x=1

Homework Equations

The Attempt at a Solution

f(1)=g(1)

I know how to evaluate definite integrals and indefinate too, but i don't understand what it means by "evaluate the integral" in the question? I only see a derivative.

To my understanding...

$$\frac{d}{dx}\right)(f^(^3^)(x^1^/^2))|$$ x=1 ...
$$= f^(^4^)(x^1^/^2)$$

So...
$$\frac{d}{dx}\right)(f^(^3^)(x^1^/^2))=\frac{d^4y}{dx^4}\right)$$

And multiplying the differential dx and integrating the integrand $$f^(^4^)$$ will give you $$f^(^3^)(x^1^/^2)$$ so somehow I am suppose to integrate $$f^(^3^)(x^1^/^2)$$ until I get to f`(x) which should equal 5 or -1/3?

I honestly don't understand the how to even start what the question is asking me. I just transferred to a different school and the professor already taught basic definite and indefinite integration in calculus I which I never learned in my calculus I class.

?:|

 

[LCKurtz]

What does g have to do with it? Are you sure you have stated the problem correctly?

 

[Samuelb88]

Yes, I just read the question again and it's word for word. It's has a part A and B, but part b has no function g either. *shrug*