Final answer:
The solution involves reversing the order of integration by redefining the limits of integration based on the other variable. A precise solution requires the specific limits for the integral, which are missing in the question. The process includes integrating with respect to the first variable, then with respect to the second, according to the new limits.
Step-by-step explanation:
To evaluate the integral by reversing the order of integration for \(-3 < y < 3, \cos(2x^2)\, dx\, dy\), we would first need the specific limits of the integral for both variables x and y. The question seems to be missing these details, which are necessary to proceed with the solution. However, I can provide a general approach to the problem.
Reversing the order of integration typically involves determining the boundaries of the region of integration in terms of the other variable. For example, if the integral is first given in terms of dx with y as a constant, when reversing the order, we will need to express x in terms of y and adjust the limits of integration accordingly.
Next, we would integrate the inner integral holding y constant and then integrate the resulting function with respect to y following the new limits for y. The process requires understanding the geometry of the region of integration as well as the functions involved to ensure the new limits correctly represent the original region.