A Whole Family, and the One You Want

You'll learnto run each derivative rule backwards, to keep the constant that comes with it, and to check any answer in seconds by differentiating what you wrote.

A definite integral asks how much. An indefinite one asks which function, and the answer is never one function: it is a whole family, spaced by constants, all with the same derivative. Everything else here is a derivative rule read from right to left, so every answer can be checked by differentiating it back. A wrong antiderivative is a curve whose slope comes out at the wrong height. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · DIFFERENTIATE WHAT YOU WROTE AND COMPARE · v2

antidifferentiate, keep the constant, then differentiate what you wrote

Before you start

What you're looking at

One plot panel. Blue is always the function being antidifferentiated; pink is an antiderivative of it; yellow is the measured slope of a candidate answer and red the slope of a wrong one.

The question

What does an indefinite integral actually name, and how do you tell in seconds whether what you wrote down is one?

Step 1 / 12