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

Integrate ((-2x)/(2(9-1x^2)^0.5))^2^0.5 from -1 to 2

Answer

$-\frac{1}{3}\int_{-1}^{2}9\sin\left(\theta\right)d\theta$

Step-by-step explanation

Problem

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

Applying the power of a power property

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

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Answer

$-\frac{1}{3}\int_{-1}^{2}9\sin\left(\theta\right)d\theta$

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

Main topic:

Integration by trigonometric substitution

Used formulas:

3. See formulas

Time to solve it:

~ 9.76 seconds