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Evaluate $$\iint_D\ e^{-x^2 - y^2}\ dA,$$ where $D$ is annulus $a \le x^2 + y^2 \le b$

My understanding is it involves polar coordinates but I don't understand how to convert it.

Xoque55
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mathymath
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1 Answers1

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Since $r^2 = x^2 + y^2$ (do you see why?), we're considering the annulus $\sqrt{a} \le r \le \sqrt{b}$. Then the integral is

$$\iint_D\ e^{-r^2}\ dA,$$

The area element is $dA = r\ dr\ d\theta$ in polar coordinates. Now what do you make the limits of integration?

zahbaz
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