Find the average value over the given interval.
\[
y=9 e^{-x} ;[0,5]
\]
The average value is (Type an exact answer.)

Answer

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

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Step 1 ：The average value of a function over an interval [a, b] is given by the formula: \(\frac{1}{b-a} \int_{a}^{b} f(x) dx\)

Step 2 ：In this case, the function is \(y = 9e^{-x}\) 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: \(average\_value = 1.8 - 1.8*exp(-5)\)

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

Find the average value over the given interval.\[y=9 e^{-x} ;[0,5]\]The average value is (Type an exact answer.)

Answer

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Find the average value over the given interval.
\[
y=9 e^{-x} ;[0,5]
\]
The average value is (Type an exact answer.)