$\"\"$

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The integral is $\"\"$ .

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Rewrite the integral as $\"\"$ .

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Consider $\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$ .

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$\"\"$

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Substiute the corresponding values in the integral.

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$\"\"$

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$\"\"$

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$\"\"$

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Apply double angle formula : $\"\"$ .

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$\"\"$

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$\"\"$ .

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If $\"\"$ then $\"\"$

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$\"\"$ .

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(a) Apply integration limits.

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$\"\"$

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$\"\"$

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

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(b)

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Apply trigonometric limits in equation $\"\"$ .

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$\"\"$ .

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If $\"\"$ then $\"\"$ .

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If $\"\"$ then $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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(a) By the integration limits : $\"\"$ .

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(b) By the limits obtained by the trigonometric substitution: $\"\"$ .