Question

Notation: Describe the meanings of each of the following mathematical expressions or how they are commonly used in this chapter:

${\int }_a^{b}f\left(x\right)dx$.

Short answer

If $f$is continuous on the interval $\left[a,b\right]$and $F$is any antiderivative of $f$, then

${\int }_a^{b}f\left(x\right)dx=F\left(b\right)-F\left(a\right)$.

Step-by-step solution

Step 1. Given information 

${\int }_a^{b}f\left(x\right)dx$.

Step 2. Definition for the given expression.

If $f$is continuous on $\left[a,b\right]$and $F$is any antiderivative of $f$, then

${\int }_a^{b}f\left(x\right)dx=F\left(b\right)-F\left(a\right)$