Question

Find the average value of the function on the given interval.
f(x)=e0.1x; [1,13]

Answer 1

2.13677

Explanation:

Given function in the question:

f(x) =
`e^(0.1x)` ; [1 , 13]

Now,

The average value is calculated as:

⇒
`(1)/(b-a)\int\limits^b_a {f(x)} \, dx`

Therefore,

for the given data

a = 1

b = 13

f(x) =
`e^(0.1x)`

Thus,

average =
`(1)/(13-1)\int\limits^(13)_1 {e^(0.1x)} \, dx`

or

average =
`(1)/(12)*[(e^(0.1x))/(0.1)]^(13)_1`

or

average =
`(1)/(12)*[(e^(0.1(13)))/(0.1)-(e^(0.1(1)))/(0.1)]`

or

Average =
`(1)/(12)*` [36.693 - 11.05176]

Average =
`(1)/(12)*` 25.64124

or

Average = 2.13677