Constant of integration calculator

Integration is a way of adding slices to find the whole.

Integration can be used to find areas, volumes, central points and many useful things.

But it is easiest to start with finding the area between a function and the x-axis like this:

What is the area?

Slices

We could calculate the function at a few points and add up slices of width Δx like this (but the answer won't be very accurate):
We can make Δx a lot smaller and add up many small slices (answer is getting better):
And as the slices approach zero in width, the answer approaches the true answer. We now write dx to mean the Δx slices are approaching zero in width.

That is a lot of adding up!

But we don't have to add them up, as there is a "shortcut", because ...

...

finding an Integral is the reverse of finding a Derivative.

(So you should really know about Derivatives before reading more!)

Like here: