Problem

Let

$$D=\{(x,y):x\ge 0,\ y\ge 0,\ 0\le x^2+4y^2\le 4\}$$

and let

$$f(x,y)=\frac{3}{\pi}\sqrt{x^2+4y^2}$$

for $(x,y)\in D$. Which of the following statements is true?

(a) $-\infty<\int_D f(x,y)\,d(x,y)\le 2$.

(b) $2<\int_D f(x,y)\,d(x,y)\le 4$.

(c) $4<\int_D f(x,y)\,d(x,y)\le 6$.

(d) $6<\int_D f(x,y)\,d(x,y)\le 8$.

(e) None of the above statements is true.