$\"\"$

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

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(a)

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

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$\"\"$

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(b)

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Find $\"\"$ such that $\"\"$ .

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Consider $\"\"$ .

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$\"\"$

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We have $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$ .

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Since it is very difficult to find the roots by solving the trigonometric equation, use the graph to find $\"\"$ value.

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Graph:

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Graph the functions $\"\"$ and $\"\"$ .

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$\"\"$

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From the graph,

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It is observed that, intersection points are $\"\"$ and $\"\"$ .

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The values of $\"\"$ are $\"\"$ -coordinates of the points.

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

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$\"\"$

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(c)

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Graph the function $\"\"$ and rectangle under the interval $\"\"$ .

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$\"\"$

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$\"\"$

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(a)

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

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(b) The values of $\"\"$ are $\"\"$ and $\"\"$ .

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(c) Graph:

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$\"\"$ .