Luke B. answered • 03/14/19
My goal is to help you succeed in math and learn to love math!
Hello! Great question. I’ll try to sum it up for you.
The short answer is that a derivative and an integral are opposites of each other. Another name for an integral is an antiderivative, which literally implies that it is the opposite. I don’t know how much detail you are looking for, but if you are familiar with the Fundamental Theorem of Calulus, this states that if you have a function and you take the integral and then the derivative of that integral, or take the derivative then the integral of the dervative, you get back your original function indicating that they “cancel” or are opposites.
In terms of function, here is how they are different:
When you take a derivative, you are finding the slope of a function at any given point. When you take an integral, you are finding the area under the curve over a certain interval.
Hope this helps! Feel free to reach out with any other questions.
