1. The question asks why we might not integrate with respect to $x$ first in a given problem. 2. When performing double integrals, the order of integration depends on the region of integration and the function. 3. Sometimes integrating with respect to $x$ first is complicated due to the limits or the integrand. 4. We choose the order that simplifies the integral, often integrating with respect to the variable that makes the inner integral easier. 5. For example, if the limits for $y$ are constants but for $x$ depend on $y$, integrating with respect to $y$ first might be simpler. 6. The key is to analyze the region and integrand to decide the best order of integration.