Chapter 9 - Integration

MATH1050Calculus This chapter is not fully complete yet and might remain as is.

9.1 Antiderivatives and Indefinite Integrals

A function $F$ is called an antiderivative of $f$ on an interval $I$ if $F^{\prime }(x)=f(x)$ for all $x\in I$.

For example,

$$F(x)=2x^3\text{ is an antiderivative of }f(x)-6x^2$$

for all $x\in \mathbb{R}$ since $F^{\prime }(x)=6x^2=f(x)$ for all $x\in \mathbb{R}$. However, $F(x)=2x^3+10$ is also an antiderivative of $f(x)=6x^2$ for all $x\in \mathbb{R}$.