Explanation Given: The given function is f ( x , y ) = 9 − y 2 . Formula used: The area of the surface z = f ( x , y ) is: A = ∬ R 1 + [ f x ( x , y ) ] 2 + [ f y ( x , y ) ] 2 Calculation: The triangle formed by joining the given vertices is: The line equation joining the vertices ( − 3 , 3 ) and ( 0 , 0 ) is: y = x 2 − x 1 y 2 − y 1 x = 0 − ( − 3 ) 0 − 3 x = 3 − 3 x = − x The line equation joining the vertices ( 3 , 3 ) and ( 0 , 0 ) is: y = x 2 − x 1 y 2 − y 1 x = 0 − ( 3 ) 0 − 3 x = 3 3 x = x Now, consider f ( x , y ) = 9 − y 2 . Differentiate partially the above equation with respect to x gives: ∂ ∂ x f ( x , y ) = ∂ ∂ x ( 9 − y 2 ) f x ( x , y ) = 0 Differentiate partially the equation f ( x , y ) = 9 − y 2 with respect to y gives: ∂ ∂ y f ( x , y ) = ∂ ∂ y ( 9 − y 2 ) f y ( x , y ) = − 2 y Now, from the given region the limit of x must be − y to y . And the limit of y must be 0 to 3

Calculus: Early Transcendental Functions

7th Edition

ISBN: 9781337552516

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 14, Problem 45RE

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To calculate: The area of the surface given by f(x,y)=9−y2.that lies above the triangle with vertices (−3,3),(0,0)and(3,3).

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Chapter 14, Problem 44RE

Chapter 14, Problem 46RE

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Chapter 14 Solutions

Calculus: Early Transcendental Functions

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The area of the surface given by f ( x , y ) = 9 − y 2 .that lies above the triangle with vertices ( − 3 , 3 ) , ( 0 , 0 ) and ( 3 , 3 ) .

Solution Summary: The author calculates the area of the surface given by f(x,y)=9-y

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To calculate: The area of the surface given by f(x,y)=9−y2.that lies above the triangle with vertices (−3,3),(0,0)and(3,3).

Want to see the full answer?

Chapter 14 Solutions