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Chapter 14, Problem 44RE
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### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Finding Surface AreaIn Exercises 43–46, find the area of the surface given by z = f ( x , y ) that lies above the region R f ( x , y ) = 8 + 4 x − 5 y R = { ( x , y ) : x 2 + y 2 ≤ 1 }

To determine

To calculate: Find out the Surface Area specified by z=f(x,y) and located above the region R

f(x,y)=8+4x5yR={(x,y):x2+y21}

Explanation

Given:

Surface function: f(x,y)=8+4xâˆ’5y

Region below the surface: R={(x,y):x2+y2â‰¤1}

Formula used:

Surface Area: S.A=âˆ¬Rfx2+fy2+1dA

Where,

fx=âˆ‚f(x,y)âˆ‚x and fy=âˆ‚f(x,y)âˆ‚y

Calculation:

Consider the figure of region below the surface R={(x,y):x2+y2â‰¤1} and the surface function is, f(x,y)=8+4xâˆ’5y

Partial derivative,

fx=4;fy=âˆ’5

Put the values into formula of surface area,

S

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