Q. 7 - Calculus

Question

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

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

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

Step-by-Step Solution

Answer

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

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

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 $x\in [a,b]$ 

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