Antiderivatives

Running derivatives backwards

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• An antiderivative $F$ of $f$ satisfies $F' = f$. All antiderivatives differ by a constant $C$.
• $\int x^n\,dx = \frac{x^{n+1}}{n+1} + C$ for $n \ne -1$.
• A starting value (like $h(0)$) fixes $C$.

Steps

1. Reverse it
2. Only one?
3. Reverse power rule
4. Practice
5. Find C
6. Pick the right curve
7. Negative powers