Final answer:
The crucial step when evaluating the integral by changing the order of integration is choosing the appropriate variable of integration.
Step-by-step explanation:
The crucial step when evaluating the integral by changing the order of integration is B) Choosing the appropriate variable of integration.
When changing the order of integration, we need to select the appropriate variable of integration based on the given integrand and the region of integration. This choice will make the integral easier to evaluate and often leads to simplifications.
For example, if we have an integral with limits of integration in terms of x and y, and the integrand involves functions of both x and y, we can choose to integrate with respect to x first and then integrate with respect to y. Conversely, we can choose to integrate with respect to y first and then integrate with respect to x. This choice depends on the nature of the integrand and the region of integration.