Find the Exact Area of the Surface $z = x ^ { 2 } + 2 y , 0 \leq x \leq 1,0 \leq y \leq 2$

Multiple Choice

Find the exact area of the surface. $z = x ^ { 2 } + 2 y , 0 \leq x \leq 1,0 \leq y \leq 2$ .

A) $\frac { 5 \ln ( 3 ) } { 4 }$
B) $\frac { 5 } { 4 }$
C) $3 - \ln ( 5 )$
D) $3 + \frac { 5 } { 4 } \ln ( 5 )$
E) $2 + \frac { 5 } { 3 } \ln ( 4 )$