Question

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

7. If $f$is on $[a,b]$, then for all $x\in [a,b]$

localid="1648820555152" $\frac{d}{dx}{\int }_a^{x}f\left(t\right)dt=\_\_\_\_$

Short answer

If $f$is on $[a,b]$, then for alllocalid="1648820602757" $x\in [a,b]$

localid="1648821198091" $\frac{d}{dx}{\int }_a^{x}f\left(t\right)dt=f\left(x\right)$

Step-by-step solution

Step 1. Given information

We have to complete the statement,

If $f$is on $[a,b]$, then for all$x\in [a,b]$

$\frac{d}{dx}{\int }_a^{x}f\left(t\right)dt=\_\_\_\_$

Step 2. Fill in the blanks

If $f$is on $[a,b]$, then for all $x\in [a,b]$

localid="1648821183890" $\frac{d}{dx}{\int }_a^{x}f\left(t\right)dt=f\left(x\right)$