Final answer:
To solve a polar integral with no variables in the boundaries, one can convert to Cartesian coordinates, use a double integral in rectangular coordinates or, if appropriate, integrate with respect to the polar angle.
Step-by-step explanation:
When attempting to solve an integral where the boundaries do not contain a variable, and you are working in polar coordinates, the trick with polars is typically one of the following: you can either convert the integral to Cartesian coordinates, use a double integral in rectangular coordinates, or if the variables simplify nicely, integrate with respect to the polar angle. It should be noted that thinking the integral is unsolvable, and thus skipping it, is not a correct option, as even challenging integrals have solutions using appropriate methods.
The choice between these options depends on the specific problem. Converting to Cartesian coordinates might help if the problem becomes simpler in that coordinate system. Using a double integral in rectangular coordinates could be advantageous when the shape or region of interest aligns more naturally with a Cartesian grid. Integrating with respect to the polar angle is suitable when the problem involves circular symmetry, or the integral's limits are defined by angles.