Derivative and Integration

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

Note: Use the simple function given below.

f(x) = x^2

 

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”.

 

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

 

I didn't expect a complicated reply.

 

Interestingly difficult.

 

it's not algebra

 

It's calculus but I wanted to learn at least this much of the course. I do miss calculus 1.