Question

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

Answer 1

`f_(avg)=e-1`

Explanation:

We are given that a function

`f(x)=e^{(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

`(1)/(b-a)\int_(a)^(b)f(x)dx`

Using the formula

`f_(avg)=(1)/(7-0)\int_(0)^(7)e^{(x)/(7)} dx`

`f_(avg)=(1)/(7)[e^{(x)/(7)}* 7)]^(7)_(0)`

By using the formula

`\int e^(ax)=(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`