Explanation Given Info: Given G ( u , v ) = ( u 2 − v 2 , u + v , u − v ) . f ( x , y , z ) = 1 . Formula Used: Let G ( u , v ) be a parametrization of a surface S with parameter domain D . Assume that G is continuously differentiable, one-to-one, and regular (except possibly at the boundary of D ). Then, ∬ S f ( x , y , z ) d S = ∬ D f ( G ( u , v ) ) ‖ N ( u , v ) ‖ d u d v . Where N ( u , v ) = T u × T v , T u = ∂ G ∂ u , T v = ∂ G ∂ v Calculation: T u = ∂ ( u 2 − v 2 , u + v , u − v ) ∂ u T u = ( 2 u , 1 , 1 ) T v = ∂ ( u 2 − v 2 , u + v , u − v ) ∂ v T v = ( − 2 v , 1 , − 1 ) N ( u , v ) = i j k 2 u 1 1 − 2 v 1

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 17.4, Problem 11E

To determine

To estimate: The area $\iint_{S} d S$ of small patch of surface $G (u, v) = (u^{2} - v^{2}, u + v, u - v)$ defined by $2 \leq u \leq 2.1, 3 \leq v \leq 3.2$ .

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Chapter 17.4, Problem 10E

Chapter 17.4, Problem 12E

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Chapter 17 Solutions

CALCULUS (CLOTH)

Ch. 17.1 - Prob. 1PQ Ch. 17.1 - Prob. 2PQ Ch. 17.1 - Prob. 3PQ Ch. 17.1 - Prob. 4PQ Ch. 17.1 - Prob. 1E Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E Ch. 17.1 - Prob. 6E

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To estimate: The area ∬ S d S of small patch of surface G ( u , v ) = ( u 2 − v 2 , u + v , u − v ) defined by 2 ≤ u ≤ 2.1 , 3 ≤ v ≤ 3.2 .

Solution Summary: The author calculates the area S d S of a small patch of surface G ( u, v ) with parameter domain D. Assume that G is continuously differentiable, one-to-

Concept explainers

Videos

To estimate: The area $\iint_{S} d S$ of small patch of surface $G (u, v) = (u^{2} - v^{2}, u + v, u - v)$ defined by $2 \leq u \leq 2.1, 3 \leq v \leq 3.2$ .

Want to see the full answer?

Chapter 17 Solutions

To estimate: The area ∬ S d S of small patch of surface G ( u , v ) = ( u 2 − v 2 , u + v , u − v ) defined by 2 ≤ u ≤ 2.1 , 3 ≤ v ≤ 3.2 .

Solution Summary: The author calculates the area S d S of a small patch of surface G ( u, v ) with parameter domain D. Assume that G is continuously differentiable, one-to-

Concept explainers

Videos

To estimate: The area ∬SdS of small patch of surface G(u,v)=(u2−v2,u+v,u−v) defined by 2≤u≤2.1,3≤v≤3.2.

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Chapter 17 Solutions

To estimate: The area $\iint_{S} d S$ of small patch of surface $G (u, v) = (u^{2} - v^{2}, u + v, u - v)$ defined by $2 \leq u \leq 2.1, 3 \leq v \leq 3.2$ .