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Find the average value of the function g(x)= 5xe^{-x^2} on the interval [0,5]

Question:

Find the average value of the function {eq}g(x)= 5xe^{-x^2} {/eq} on the interval {eq}[0,5] {/eq}

Average Value of a Function:

Average value of a function {eq}f(x) {/eq} is: {eq}\displaystyle f_{avg} = \dfrac{1}{b-a} \int_{a}^{b} f(x) \ dx {/eq}

To solve the definite integral, we'll apply u-substitution. Next, compute the boundaries to get the average value of the function.

Answer and Explanation:

The average value of the function {eq}f(t) = 5xe^{-x^2} {/eq} over the interval {eq}[0, \; 5] {/eq} is:

{eq}\displaystyle...

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