3. Convert to polar coordinates to evaluate $\int_0^3 \int_0^{\sqrt{9-x^2}} e^{-(x^2+y^2)/2} \, dx \, dy$.
a. First, sketch the region of integration in the rectangular coordinate system, then
in the polar coordinate system..
b. Write the equations used to convert from rectangular to polar coordinates:
$x = $
$y = $
$x^2 + y^2 = $
c. Write $dA = dx \, dy$ in polar form: $dA = $
d. Convert the integrand to polar form: $e^{-(x^2+y^2)/2} = $
e. Rewrite the original double integral as a double integral in polar coordinates. Use
your drawings from part a to determine the limits of integration for each polar
variable:
f. Now evaluate the integral you got in part e.
