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Evaluate
Solution:
If you examine the given equation, we cannot integrate it by simple integration. Since the given equation has √ 4 - x2 , then we have to use the Trigonometric Substitution. Trigonometric Substitution is applicable if a function contains √ a2 - x2 , √ a2 + x2 , and √ x2 - a2 .
First, draw a right triangle to represent √ 4 - x2 as follows
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Let
Substitute these values to the given equation, we have
Substitute the values of θ, Sin θ, and Cos θ to the above equation, we have
Substitute the value of the limits to the above equation, we have
Therefore,
