# Thread: Correlation between integrals and differentials

1. ## Correlation between integrals and differentials

Hi MHF!

I'm wondering...Can you tell me why a definite integral is the opposite of a derivative? How can an area be the opposite of a slope? Are we going from first to 2nd dimension somehow...? If so, why?

Thanks!

2. ## Re: Correlation between integrals and differentials

The slope of the area S(x) under the graph of f(x) is again f(x). Indeed, the slope of the area is the speed with which the area increases: (S(x+h) - S(x))/h. But S(x+h) ≈ S(x) + f(x) * h, so (S(x+h) - S(x))/h ≈ f(x).

3. ## Re: Correlation between integrals and differentials

Are you familiar with the Fundamental Theorem of Calculus? If not, I would recommend checking out Wikipedia. It offers a good visualization of the theorem.