Consider the integral

${\displaystyle \underset{0}{\overset{3}{}}}{\displaystyle \underset{y}{\overset{\sqrt[\phantom{2}]{25-y^2}}{}}}{e}^{x^2{y}^{2}5}dxdy$

To evaluate this integral, we must convert it to polar coordinates. This requires splitting the region of integration into two parts, resulting in a sum of two polar integrals:

${}_{D_1}f(r,)dA{}_{D_2}f(r,)dA$

Please provide the integrand and the bounds for these two integrals.

Note: You may use "theta" for $,"$pi$"$ for $,$ and standard functions like sin $0.$ asin $0.$

a$)$ The Integrand

The integrand in polar coordinates is $f(r,)=$

b$)$ Bounds for the first integral $($the circular sector region$)$

The integration with respect to $r$ is from $$ to $$

The integration with respect to $$ is from

c$)$ Bounds for the second integral $($the remaining region$)$

The integration with respect to $r$ is from $$ to $\frac{3}{sin(\text{t}\text{h}\text{e}\text{n}\text{t}\text{a})}$

The integration with respect to $$ is from $$ to $$