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arlik [135]
3 years ago
5

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

Mathematics
1 answer:
Anastaziya [24]3 years ago
8 0

Answer:

f_{avg}=e-1

Step-by-step explanation:

We are given that a function

f(x)=e^{\frac{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

\frac{1}{b-a}\int_{a}^{b}f(x)dx

Using the formula

f_{avg}=\frac{1}{7-0}\int_{0}^{7}e^{\frac{x}{7}} dx

f_{avg}=\frac{1}{7}[e^{\frac{x}{7}}\times 7)]^{7}_{0}

By using the formula

\int e^{ax}=\frac{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

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