Find the Area of the Surface Given By $f ( x , y ) = 5 - x ^ { 2 }$

Multiple Choice

Find the area of the surface given by $f ( x , y ) = 5 - x ^ { 2 }$
$R$ : rectangle with vertices $( 0,0 ) , ( 5,0 ) , ( 5,5 ) , ( 0,5 )$

A) $\frac { 5 } { 4 } ( 10 \sqrt { 101 } - \ln ( 10 + \sqrt { 101 } ) )$
B) $\frac { 5 } { 4 } ( 10 \sqrt { 101 } + \ln ( 10 - \sqrt { 101 } ) )$
C) $5 \left( 5 \sqrt { 101 } + \frac { 1 } { 2 } \ln ( 5 + \sqrt { 101 } ) \right)$
D) $5 \left( 5 \sqrt { 101 } - \frac { 1 } { 2 } \ln ( 5 + \sqrt { 101 } ) \right)$
E) $\frac { 5 } { 4 } ( 10 \sqrt { 101 } + \ln ( 10 + \sqrt { 101 } ) )$