Math 7B - Calculus for Life Science II: Section 5.10 Antiderivatives

Vocabulary and core concepts covering Section 5.10 Antiderivatives from Math 7B Calculus for Life Science II.

Antiderivative

A function $F(x)$ is called an antiderivative of $f(x)$ if $F'(x) = f(x)$.

Generalized Antiderivative

An expression of the form $F(x) + C$, where $C$ is an arbitrary constant, representing all antiderivatives of a function $f(x)$ because the derivative of any constant is $0$.

Antiderivative of $3x^2$

$x^3$ (or generally $x^3 + C$), because $(x^3)' = 3x^2$.

Antiderivative of $\text{cos}(x)$

$\text{sin}(x)$, because $(\text{sin}(x))' = \text{cos}(x)$.

Antiderivative of $e^x$

$e^x$, because $(e^x)' = e^x$.

Antiderivative of $x^5$

$\frac{1}{6}x^6$, because $\big(\frac{1}{6}x^6\big)' = x^5$.

Generalized Antiderivative of $\text{sin}(x)$

$-\text{cos}(x) + C$, because $(-\text{cos}(x))' = \text{sin}(x)$.