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

User Bjonen
by
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1 Answer

5 votes

Answer:


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

User Rwb
by
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