# How do you find the integral of #(x^2)/(sqrt(4-(9(x^2))) #?

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To find the integral of ( \frac{x^2}{\sqrt{4-9x^2}} ), use the trigonometric substitution method. Let ( x = \frac{2}{3}\sin(\theta) ). Then, ( dx = \frac{2}{3}\cos(\theta) , d\theta ). Substitute these into the integral and simplify. You'll end up with ( \int \frac{4\sin^2(\theta)}{\sqrt{4 - 4\sin^2(\theta)}} , d\theta ). Use a trigonometric identity to simplify this to ( \int \frac{4\sin^2(\theta)}{\sqrt{4\cos^2(\theta)}} , d\theta ). Then, integrate using a trigonometric identity, and finally, substitute back ( x = \frac{2}{3}\sin(\theta) ) 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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