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Answer

$--\frac{1}{2}\int_{-1}^{2} u^{-\frac{1}{2}}du$

Step-by-step explanation

Problem to solve:

$\int_{-1}^{2}\sqrt{\left(\frac{-2x}{2\sqrt{9-x^2}}\right)^2}dx$
1

Applying the power of a power property

$\int_{-1}^{2}\frac{-2x}{2\sqrt{9-x^2}}dx$
2

Take out the constant $\frac{-2}{2}$ from the fraction

$\int_{-1}^{2}-\left(\frac{x}{\sqrt{9-x^2}}\right)dx$

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Answer

$--\frac{1}{2}\int_{-1}^{2} u^{-\frac{1}{2}}du$
$\int_{-1}^{2}\sqrt{\left(\frac{-2x}{2\sqrt{9-x^2}}\right)^2}dx$

Main topic:

Definite integrals

Used formulas:

4. See formulas

Time to solve it:

~ 1.03 seconds