Given region is {(x, y): 9x2 + y2 ≤ 36 and 3x + y ≥ 6}
We draw the curves corresponding to equations
9x2 + y2 = 36 or
\(\frac{x^2}4+\frac{y^2}{36}=1\) and 3x + y = 6
The curves intersect at (2, 0) and (0, 6)
\(\therefore\) Shaded area is enclosed by the two curves and is