Answer:
[tex]f_{avg}=e-1[/tex]
Step-by-step explanation:
We are given that a function
[tex]f(x)=e^{\frac{x}{7}}[/tex]
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
[tex]\frac{1}{b-a}\int_{a}^{b}f(x)dx[/tex]
Using the formula
[tex]f_{avg}=\frac{1}{7-0}\int_{0}^{7}e^{\frac{x}{7}} dx[/tex]
[tex]f_{avg}=\frac{1}{7}[e^{\frac{x}{7}}\times 7)]^{7}_{0}[/tex]
By using the formula
[tex]\int e^{ax}=\frac{e^{ax}}{a}[/tex]
[tex]f_{avg}=(e-e^0)=e-1[/tex]
Because [tex]e^0=1[/tex]
[tex]f_{avg}=e-1[/tex]
Hence, the average value of function on interval [0,7]
[tex]f_{avg}=e-1[/tex]
