Convert the integral

$I={\displaystyle \underset{0}{\overset{\frac{2}{\sqrt[\phantom{2}]{2}}}{}}}{\displaystyle \underset{y}{\overset{\sqrt[\phantom{2}]{4-y^2}}{}}}{e}^{7x^2+7y^2}dxdy$

to polar coordinates, getting

${\displaystyle \underset{C}{\overset{D}{}}}{\displaystyle \underset{A}{\overset{B}{}}}h(r,)drd$

where

$h(r,)=$

$$

$A=$

$B=$

$C=$

$D=$

and then evaluate the resulting integral to get

$I=$