Find the average of the function $f ( x ) = e ^ { x }$ over $[ 0,8 ]$ .
A)Average = $1 - e ^ { 8 }$
B) Average = $\frac { e ^ { - 8 } } { 8 }$
C) Average = $\frac { 1 + e ^ { - 8 } } { 8 }$
D) Average = $\frac { e ^ { 8 } - 1 } { 8 }$
E) Average = $1 - e ^ { - 8 }$

Question

Find the average of the function $f ( x ) = e ^ { x }$ over $[ 0,8 ]$ .  
A)Average = $1 - e ^ { 8 }$
B) Average = $\frac { e ^ { - 8 } } { 8 }$
C) Average = $\frac { 1 + e ^ { - 8 } } { 8 }$
D) Average = $\frac { e ^ { 8 } - 1 } { 8 }$
E) Average = $1 - e ^ { - 8 }$

Quizplus · Accepted Answer

The average value of a function $f(x)$ over the interval $[a, b]$ is given by $\frac{1}{b-a} \int_{a}^{b} f(x) dx$. For $f(x) = e^x$ over $[0, 8]$, the average value is $\frac{1}{8-0} \int_{0}^{8} e^x dx = \frac{1}{8} [e^x]_{0}^{8} = \frac{e^8 - e^0}{8} = \frac{e^8 - 1}{8}$.

Find the Average of the Function f(x)=exf ( x ) = e ^ { x }f(x)=ex

Find the Average of the Function $f ( x ) = e ^ { x }$