Question

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

Answer 1

Answer:

2.13677

Step-by-step explanation:

Given function in the question:

f(x) = $e^{0.1x}$             ; [1 , 13]

Now,

The average value is calculated as:

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

Therefore,

for the given data

a = 1

b = 13

f(x) = $e^{0.1x}$  

Thus,

average = $\frac{1}{13-1}\int\limits^{13}_1 {e^{0.1x}} \, dx$

or

average = $\frac{1}{12}\times[\frac{e^{0.1x}}{0.1}]^{13}_1$

or

average = $\frac{1}{12}\times[\frac{e^{0.1(13)}}{0.1}-\frac{e^{0.1(1)}}{0.1}]$

or

Average =  $\frac{1}{12}\times$ [36.693 - 11.05176]

Average =  $\frac{1}{12}\times$ 25.64124

or

Average = 2.13677