Question

What is the difference between derivatives and integration?

Answer 1

They are opposites of each other...

Explanation:

Say I have a position `x` of a particle, then we define the velocity of the particle to be `(dx)/(dt)`, where `t` represents the time in seconds.

Now, let's say I have the velocity of the particle as `v`, then the position of the particle would be `intv \ dt`.

Let's try another example if that wasn't clear enough.

The derivative of `x^2` is `(x^2)'=2x`.

Now, the integral of `2x` would be `int2x \ dx=x^2+C`, where `C` is constant.

I hope you can figure it out from here!

Answer 2

There is a nice history about this topic

Explanation:

Isaac Newton and G Leibnitz discovered these concepts almost at the same time (12 years of diference in XVII century)
Derivative is looking for instant variation of a function. and means the slope of a tangent line of the graph of the function in every point

Integral is looking for the area under a graph

Barrow's rule proves that this pair of problems are inverse one of each other