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Need to verify $\"\"$ .

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(a) $\"\"$

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Evaluate the integral $\"\"$ by using trigonometric substitution method:

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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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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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Take the limits:

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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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From part (a) the equation is $\"\"$ .

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The two parts are $\"\"$ and $\"\"$ .

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Left hand side of the above equation $\"\"$ is represents the area under the curve $\"\"$ between the

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vertical lines $\"\"$ and $\"\"$ .

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$\"\"$

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Observe the figure shows that this area consists of a triangular region and a sector of the circle.

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$\"\"$ .

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Formula for the triangle area is $\"\"$ .

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$\"\"$

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$\"\"$ .

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This is one part of the right hand side equation.

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Formula for the the sector area is $\"\"$ .

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

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$\"\"$

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This is one part of the right hand side equation.

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$\"\"$ .