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

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

Short 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

role="math" localid="1648818554518" ${\int }_a^b{f}^{\text{'}}\left(x\right)dx=f\left(b\right)-f\left(a\right)$

Step-by-step solution

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

role="math" localid="1648818562893" ${\int }_a^b{f}^{\text{'}}\left(x\right)dx=f\left(b\right)-f\left(a\right)$