## Fundamental Theorem of Calculus

This theorem forms much of the basis of calculus and the uses of differentiation and integration. It basically states that differentiation and integration are opposites so if you differentiate and integral you’ll get the function you started with. This can be stated as follows:

if then

or in the more simple case

if then

It is this idea that allows us to know, for example,

from the knowledge that

\

This makes much of integration easier as it is often much easier to work out the derivative a function than work out the integral of one so we can look for functions which when differentiated give us the function that we want to integrate and then know that the integral is that function plus a constant.

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Categories: calculus, maths
calculus, differentiation, fundamental theorem, integration

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