Q. 3 - Calculus

Question

Fill in the blanks to complete each of the following theorem statements: 

3. The Net Change Theorem: If $f$is ____ on $[a, b]$ and its derivative $f\text{'}$ is ____ on $[a, b]$, then

${\int }_a^b{f}^{\text{'}}\left(x\right)dx=$

Step-by-Step Solution

Answer

The Net Change Theorem: If f is differentiable on $[a, b]$ and its derivative $f\text{'}$ is the area between the graph on $[a, b]$, then

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

Step 1. Given data

We have to complete the statement,

The Net Change Theorem: If f is  ____ on $[a, b]$ and its derivative $f\text{'}$ is ____ on $[a, b]$, then 

${\int }_a^b{f}^{\text{'}}\left(x\right)dx=$

Step 2. Fill the blanks

The Net Change Theorem: If $f$ is differentiable   on $[a, b]$ and its derivative $f\text{'}$ is the area between the graph  on $[a, b]$, then

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