Okay I have several questions that have been bothering me for some time now, so bear with me please.(adsbygoogle = window.adsbygoogle || []).push({});

- How does integration work? Integrating the function f(x) between the bounds a,b finds the area under f(x) between a and b. But how does this work?

If my function is f(x) = 2x and my bounds are [1,10], how come F(10) - F(1) equals the area under 2x from 1,10? (Where F(x) = x^2).

- Furthermore, why does a derivative work? The derivative of the function f(x) yields a relationship between the rate of change in f(x) and a given input. But how does this actually work?

Or put in a different way, if my function is 1x^2, why can I multiply the coefficient by the exponent to yield a function (2x) that tells me the rate at which the function will change?

- What does it mean that time is being removed (divided in a derivative) or added (multiplied in an integral)?

Thanks for reading.

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# Conceptual question of integration and derivation

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