반복적분 $\displaystyle \int _ {0} ^ {2} {\int _ {\frac{y} {2}} ^ {1} {ye ^ {x ^ {2}} dxdy}}$ 의 값은?

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