Explanation Given: The surface is given by f ( x , y ) = ln | sec x | , above the region R , which is represented by R = { ( x , y ) : 0 ≤ x ≤ π 4 , 0 ≤ y ≤ tan x } . Formula used: The surface area can be calculated of the region R by, S = ∬ R 1 + [ f x ( x , y ) ] 2 + [ f y ( x , y ) ] 2 d A Differentiation formula d d x ( x n ) = n x n − 1 , d d x ( constant ) = 0 Calculation: The function given is f ( x , y ) = ln | sec x | . Now partially differentiating it with respect to x , use d d x ( x n ) = n x n − 1 , d d x ( constant ) = 0 f x ( x , y ) = d d x ( ln | sec x | ) = 1 sec x ⋅ sec x tan x = tan x Now, with respect to y f y ( x , y ) = d d y ( ln | sec x | ) = 0 Substitute in the formula S = ∬ R 1 + [ f x ( x , y ) ] 2 + [ f y ( x , y ) ] 2 d A

11th Edition

ISBN: 9781337275347

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 14.5, Problem 11E

To determine

To calculate: The area of the surface given by z=f(x,y)=ln|secx| which lies above the region R, which is represented by R={(x,y): 0≤x≤π4,0≤y≤tanx}.

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The area of the surface given by z = f ( x , y ) = ln | sec x | which lies above the region R , which is represented by R = { ( x , y ) : 0 ≤ x ≤ π 4 , 0 ≤ y ≤ tan x } .

Solution Summary: The author calculates the surface area of the region R by sqrt2-1 units.

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To calculate: The area of the surface given by z=f(x,y)=ln|secx| which lies above the region R, which is represented by R={(x,y): 0≤x≤π4,0≤y≤tanx}.

Chapter 14 Solutions