Q. 11 - Calculus

Question

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

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

Step-by-Step Solution

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 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

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