Question

Find the average value of the function on the given interval. f(x)=ex/7; [0,7]

Answer 1

Answer:

$f_{avg}=e-1$

Step-by-step explanation:

We are given that a function

$f(x)=e^{\frac{x}{7}}$

We have to find the average value of function on the given interval [0,7]

Average value of function on interval [a,b] is given by

$\frac{1}{b-a}\int_{a}^{b}f(x)dx$

Using the formula

$f_{avg}=\frac{1}{7-0}\int_{0}^{7}e^{\frac{x}{7}} dx$

$f_{avg}=\frac{1}{7}[e^{\frac{x}{7}}\times 7)]^{7}_{0}$

By using the formula

$\int e^{ax}=\frac{e^{ax}}{a}$

$f_{avg}=(e-e^0)=e-1$

Because $e^0=1$

$f_{avg}=e-1$

Hence, the average value of function on interval [0,7]

$f_{avg}=e-1$