# How do you evaluate #int sqrt (1-x^2) dx # for [-1, 1]?

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To evaluate ( \int \sqrt{1-x^2} , dx ) for ( [-1, 1] ), use the trigonometric substitution ( x = \sin(\theta) ). Then, express ( dx ) in terms of ( d\theta ) and rewrite the integral in terms of ( \theta ). After integrating with respect to ( \theta ), convert back to the variable ( x ) to obtain the result.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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