$\"\"$

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(a)

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The reduction formula is $\"\"$ , where $\"\"$ is an integer.

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Apply limits on each side $\"\"$ to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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(b)

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The definite integral is $\"\"$ .

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From part (a): $\"\"$ .

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In this case $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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$\"\"$

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The definite integral is $\"\"$ .

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From part (a): $\"\"$ .

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In this case $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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$\"\"$

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(c) show that $\"\"$ .

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Consider $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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From part (a): $\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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$\"\"$

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(a) $\"\"$ .

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(b) $\"\"$ and $\"\"$ .

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(c) $\"\"$ .