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The integral is $\"\"$ .

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

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Find the absolute minimum and maximum values in the interval $\"\"$ .

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$\"\"$ .

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

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$\"\"$

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$\"\"$ .

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Find the critical number by equating $\"\"$ to zero.

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$\"\"$

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General solution of cosine function is $\"\"$ .

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$\"\"$

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For $\"\"$ then

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$\"\"$

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$\"\"$ is not in the interval $\"\"$ , hence it is not considered.

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$\"\"$ .

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Find the value of the function at the critical number $\"\"$ .

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$\"\"$

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Find the value of the function at the end points at $\"\"$ .

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Substitute $\"\"$ in the function.

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$\"\"$

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Substitute $\"\"$ in the function.

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$\"\"$

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Therefore, absolute minimum of the function in the $\"\"$ is $\"\"$ .

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Absolute minimum of the function in the $\"\"$ is $\"\"$ .

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$\"\"$ .

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Comparison property of integrals:

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If $\"\"$ for $\"\"$ , then $\"\"$ .

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

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By comparison property of integrals :

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$\"\"$

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$\"\"$ .