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How do you integrate #int(-12)/[x^2sqrt(4-x^2)] dx#?

Answer 1

Christopher Allers

Try this:

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Answer 2

Charles Arocha

To integrate the given expression, you can use trigonometric substitution. Let (x = 2 \sin(\theta)), (dx = 2 \cos(\theta) d\theta). After substitution, you'll get:

[\int \frac{-12}{x^2\sqrt{4-x^2}} dx = \int \frac{-12}{(2\sin(\theta))^2\sqrt{4-(2\sin(\theta))^2}} \cdot 2\cos(\theta) d\theta]

Simplify this expression and then integrate it with respect to (\theta). After integration, convert back to the original variable (x).

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Answer from HIX Tutor

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.