Antiderivatives Review

Front

Back

Front

Back

Front

Back

Front

Back

Front

Back

Front

Define an antiderivative.

Back

An antiderivative of a function f(x) is a function F(x) such that F'(x) = f(x).

Front

What is the power rule for antiderivatives?

Back

If f(x) = x^n, then the antiderivative F(x) = \frac{x^{n+1}}{n+1} + C, where n ≠ -1.

Front

Explain the constant of integration (C).

Back

The constant of integration (C) represents an infinite number of possible vertical shifts of the antiderivative.

Front

What is the antiderivative of a constant k?

Back

The antiderivative of a constant k is kx + C.

Front

How do you find the antiderivative of a polynomial function?

Back

Use the power rule for each term: increase the exponent by 1 and divide by the new exponent.