# What is the integral of dy/dx?

Dec 15, 2014

First set up the problem.

$\int \frac{\mathrm{dy}}{\mathrm{dx}} \mathrm{dx}$

Right away the two $\mathrm{dx}$ terms cancel out, and you are left with;

$\int \mathrm{dy}$

The solution to which is;

$y + C$

where $C$ is a constant.

This shouldn't be much of a surprise considering that derivatives and integrals are opposites. Therefore, taking the integral of a derivative should return the original function $+ C$