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

question 58

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) \(\frac { 5 } { 4 } ( 10 \sqrt { 101 } + \ln ( 10 + \sqrt { 101 } ) )\)

---

Definitions:

Palpebrae

The medical term for eyelids, which protect and moisturize the eyes.

Sclera

White of the eye; white, opaque portion of the fibrous tunic of the eye.

Bulbar Conjunctiva

Conjunctiva that covers the surface of the eyeball.

Blink Reflex

An involuntary blinking of the eyelids elicited by stimulation of the cornea or sudden approach of objects, serving as a protective mechanism for the eyes.