   Chapter 14, Problem 44RE

Chapter
Section
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+4x5y

Region below the surface: R={(x,y):x2+y21}

Formula used:

Surface Area: S.A=Rfx2+fy2+1dA

Where,

fx=f(x,y)x and fy=f(x,y)y

Calculation:

Consider the figure of region below the surface R={(x,y):x2+y21} and the surface function is, f(x,y)=8+4x5y

Partial derivative,

fx=4;fy=5

Put the values into formula of surface area,

S

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