Answer:
2.13677
Step-by-step explanation:
Given function in the question:
f(x) = [tex]e^{0.1x}[/tex] ; [1 , 13]
Now,
The average value is calculated as:
⇒ [tex]\frac{1}{b-a}\int\limits^b_a {f(x)} \, dx[/tex]
Therefore,
for the given data
a = 1
b = 13
f(x) = [tex]e^{0.1x}[/tex]
Thus,
average = [tex]\frac{1}{13-1}\int\limits^{13}_1 {e^{0.1x}} \, dx[/tex]
or
average = [tex]\frac{1}{12}\times[\frac{e^{0.1x}}{0.1}]^{13}_1[/tex]
or
average = [tex]\frac{1}{12}\times[\frac{e^{0.1(13)}}{0.1}-\frac{e^{0.1(1)}}{0.1}][/tex]
or
Average = [tex]\frac{1}{12}\times[/tex] [36.693 - 11.05176]
Average = [tex]\frac{1}{12}\times[/tex] 25.64124
or
Average = 2.13677
