Problem

Find the average value over the given interval.
y=9ex;[0,5]
The average value is (Type an exact answer.)

Answer

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Answer

The average value of the function over the interval [0, 5] is approximately 1.788.

Steps

Step 1 :The average value of a function over an interval [a, b] is given by the formula: 1baabf(x)dx

Step 2 :In this case, the function is y=9ex and the interval is [0, 5]. So we need to integrate the function from 0 to 5, and then divide by the length of the interval, which is 5 - 0 = 5.

Step 3 :Let's calculate the average value: average_value=1.81.8exp(5)

Step 4 :The average value of the function over the interval [0, 5] is approximately 1.788.

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