What is an Antiderivative?

In calculus, an antiderivative (or indefinite integral) is essentially the reverse process of finding a derivative. If you have a function representing the rate of change (like velocity), finding its antiderivative gives you the original function (like position).

Whenever you calculate an indefinite integral, you must always add a constant, usually denoted as + C. This is because the derivative of any constant number is zero, so when reversing the process, we don't know what constant might have originally been there.

The Power Rule for Integration

For polynomials, we use the Reverse Power Rule. To find the integral of xⁿ:

Steps to apply the rule:

1. Add 1 to the exponent.
2. Divide the entire term by the new exponent.
3. Repeat for every term in the polynomial.
4. Add "+ C" at the end.

Example: The integral of 3x² is (3x³) / 3, which simplifies to x³.

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