Consider the domain $D$ contained in the first quadrant and bound by the ellipse $\frac{x^2}{36} + \frac{y^2}{49} = 1$.
Use an appropriate change of variable (maybe two changes of variables) to help you evaluate:
$\iint_D \cos\left(\frac{x^2}{36} + \frac{y^2}{49}\right) dA$
Make sure to write a clear, complete, and detailed solution. That includes being very clear about your change(s)
of variables.