Explanation 1) Concept: If the surface is of the form x = f x , y then Surface area = ∬ D □ 1 + f x 2 + f y 2 d A Where D is the projection of the surface on the x y - plane 2) Given: The surface is, z = x 2 + 2 y 3) Calculations: It is given that surface S lies above the triangle with the vertices 0 , 0 , 1 , 0 , a n d 1 , 2 z = f x , y = x 2 + 2 y f x = 2 x f y = 2 The region D is D = x , y | 0 ≤ x ≤ 1 , 0 ≤ y ≤ 2 x Therefore, the area of the surface is A S = ∬ D □ 1 + f x 2 + f y 2 d A Substitute the above values. = ∫ 0 1 ∫ 0 2 x 1 + 2 x 2 + 2 2 d y d x = ∫ 0 1 ∫ 0 2 x 1 + 4 x 2 + 4 d y d x = ∫ 0 1 ∫ 0 2 x 4 x 2 + 5 d y d x = ∫<

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ISBN: 9781285740621

Author: James Stewart

Publisher: Cengage Learning

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Chapter 16.R, Problem 25E

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The area of the part of the surface z=x2+2y that lies above the triangle with the vertices 0, 0, 1, 0, and1, 2

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Chapter 16.R, Problem 24E

Chapter 16.R, Problem 26E

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Chapter 16 Solutions

Calculus (MindTap Course List)

Ch. 16.1 - 110 Sketch the vector field F by drawing a diagram...Ch. 16.1 - Sketch the vector field F by drawing a diagram...Ch. 16.1 - Sketch the vector field F by drawing a diagram...Ch. 16.1 - 110 Sketch the vector field F by drawing a diagram...Ch. 16.1 - 110 Sketch the vector field F by drawing a diagram...Ch. 16.1 - 110 Sketch the vector field F by drawing a diagram...Ch. 16.1 - Prob. 7E Ch. 16.1 - Prob. 8E Ch. 16.1 - Prob. 9E Ch. 16.1 - Prob. 10E

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The area of the part of the surface z = x 2 + 2 y that lies above the triangle with the vertices 0 , 0 , 1 , 0 , a n d 1 , 2

Solution Summary: The author calculates the area of the surface z=x2+2y that lies above the triangle with the vertices.

Videos

To find:

The area of the part of the surface z=x2+2y that lies above the triangle with the vertices 0, 0, 1, 0, and1, 2

Want to see the full answer?

Chapter 16 Solutions

The area of the part of the surface z = x 2 + 2 y that lies above the triangle with the vertices 0 , 0 , 1 , 0 , a n d 1 , 2

Solution Summary: The author calculates the area of the surface z=x2+2y that lies above the triangle with the vertices.

Videos

To find: The area of the part of the surface z=x2+2y that lies above the triangle with the vertices 0, 0, 1, 0, and1, 2

Want to see the full answer?

Chapter 16 Solutions

To find:

The area of the part of the surface z=x2+2y that lies above the triangle with the vertices 0, 0, 1, 0, and1, 2