Q. 2 - Calculus

Question

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

2. The Fundamental Theorem of Calculus: If $f$ is ____ on $[a, b]$, and if $F$ is any ____ of $f$, then

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

Step-by-Step Solution

Answer

The Fundamental Theorem of Calculus: If $f$ is continous on $[a,b]$, and if $F$ 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

We have to complete the statement,

The Fundamental Theorem of Calculus: If $f$ is ____ on $[a,b]$, and if $F$ is any ___ of $f$, then 

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

Step 2. Fill in the blanks

The Fundamental Theorem of Calculus: If $f$ is continuous on $[a,b]$, and if $F$ is any antiderivative of $f$, then

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