Consider the integral ${}_R{e}^{-x^2-y^2}dA$ where $R$ is the region in the third quadrant bounded between the circles $x^2{y}^2=36$ and $x^2{y}^2=49.$

Rewrite this integral in polar coordinates. Type theta to enter $$ and pi to enter $.$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}},{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}drd$

Evaluate the integral. Give an exact answer.