Evaluate $\iint _ { R } \sin \left( 9 x ^ { 2 } + 4 y ^ { 2 } \right) d A$

Essay

Evaluate $\iint _ { R } \sin \left( 9 x ^ { 2 } + 4 y ^ { 2 } \right) d A$ by making an appropriate change of variables, where R is the region in the first quadrant bounded by the ellipse $9 x ^ { 2 } + 4 y ^ { 2 } = 1$ .