$\"\"$

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The function is $\"\"$ on the interval $\"\"$ .

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

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Here $\"\"$ and $\"\"$ .

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Average value of $\"\"$ is

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$\"\"$

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Evaluate the integral using integration by parts.

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Integration by parts : $\"\"$ .

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Consider $\"\"$ .

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Differentiate on each side.

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$\"\"$ .

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Cosider $\"\"$ .

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Integrate on each side.

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$\"\"$

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$\"\"$ .

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$\"\"$ \ \

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$\"\"$

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Substitute the corresponding values in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Average value of $\"\"$ is $\"\"$ . $\"\"$

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Average value of $\"\"$ is $\"\"$ .