Thinking: Given the perimeter of the curve, the high probability will be directly used in the calculation.

Steps:

Because of the symmetry of the curve, the curve integral of 2xy is obviously 0.

In order to use the known perimeter a, we substitute the remaining formula into the integral.

For this elliptic equation, it is found that if both sides are multiplied by 12 at the same time, the same equation as the rest can be obtained.

Then, the form becomes a curve integral of 12.

The result is 12a.