# Derivative and Integration

Discussion in 'Off-Topic Chat' started by nycmathguy, Aug 3, 2022.

1. ### nycmathguy

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Show that derivative and integration are opposite
of each other. Thanks.

Note: Use the simple function given below.

f(x) = x^2

nycmathguy, Aug 3, 2022
2. ### MathLover1

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f(x) = x^2 derivate
f'(x) = 2 x integrate

This is the Fundamental Theorem of Calculus and to most people it is a very surprising result. It certainly seems strange that “to find the area under a curve” we do “the opposite of finding the gradient of the curve”.

MathLover1, Aug 3, 2022
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3. ### MathLover1

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this is the last image above if you don't see it

MathLover1, Aug 3, 2022
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4. ### nycmathguy

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I didn't expect a complicated reply.

nycmathguy, Aug 3, 2022
5. ### nycmathguy

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Interestingly difficult.

nycmathguy, Aug 3, 2022
6. ### MathLover1

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it's not algebra

MathLover1, Aug 3, 2022
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