곡선 $\displaystyle y=3+ \frac{1} {2} \cosh 2x$, $\displaystyle 0 \leq x \leq \frac{1} {2}$ 을 $y$ 축을 중심으로 회전하여 얻은 곡면의 넓이는?

• ①$\displaystyle \frac{\pi \left (e+1 \right)} {2e}$
• ②$\displaystyle \frac{\pi \left (e-1 \right)} {2e}$
• ③$\displaystyle \frac{\pi \left (e+1 \right)} {e}$
• ④$\displaystyle \frac{\pi \left (e-1 \right)} {e}$
• ⑤$\displaystyle \frac{\pi \left (2e-1 \right)} {e}$