곡면

$S= \left \{\left (x, y, z \right) \in ℝ ^ {3} \left | x ^ {2} +y ^ {2} \leq 4, z=xy \right \} \right.$

위에서 $\displaystyle \iint _ {S} \frac{z ^ {2}} {x ^ {2} + y ^ {2}} d S$ 의 값은?

• ①$\displaystyle \frac{\pi} {4} \left (\frac{5 \sqrt {5}} {3} + \frac{2} {15} \right)$
• ②$\displaystyle \frac{\pi} {4} \left (\frac{7 \sqrt {5}} {3} + \frac{2} {15} \right)$
• ③$\displaystyle \frac{\pi} {4} \left (\frac{10 \sqrt {5}} {3} + \frac{2} {15} \right)$
• ④$\displaystyle \frac{\pi} {4} \left (\frac{14 \sqrt {5}} {3} + \frac{2} {15} \right)$
• ⑤$\displaystyle \frac{\pi} {4} \left (\frac{16 \sqrt {5}} {3} + \frac{2} {15} \right)$