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!

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- October 5th 2013, 09:42 AMPazeCorrelation 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! - October 5th 2013, 10:46 AMemakarovRe: 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).

- October 5th 2013, 10:54 AMSlipEternalRe: 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.