$\"\"$

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The function is $\"\"$ and the inerval is $\"\"$ .

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Average value of the function $\"\"$ on $\"\"$ is defined as $\"\"$ .

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Here $\"\"$ .

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Average value of $\"\"$ is

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$\"\"$

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$\"\"$

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Consider $\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$ .

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Change of integral limits:

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Lower limit: If $\"\"$ then $\"\"$ .

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Upper limit: If $\"\"$ then $\"\"$ .

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Substitute $\"\"$ , $\"\"$ and change of integral limits in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Average value of the function $\"\"$ on $\"\"$ is $\"\"$ .

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$\"\"$

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Average value of the function $\"\"$ on $\"\"$ is $\"\"$ .