Evaluate the given integral by making an appropriate change of variables, where R is the region in the first quadrant bounded by the ellipse 64x2 + 81y2 = 1. $ L=\iint_{R} {\color{red}9} \sin ({\color{red}384} x^{2} + {\color{red}486} y^{2})\,dA $.

Notice that Given that is an ellipse, consider a conversion to polar coordinates:

The Jacobian for this transformation is

with determinant

Then the integral in polar coordinates is

where you can evaluate the remaining integral by substituting and .

14

step-by-step explanation:

14 x 3 = 42