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

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

See similar textbooks

Concept explainers

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic…

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along…

Triple Integral

Examples:

Videos

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 $2 \leq u \leq 2.1, 3 \leq v \leq 3.2$ .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 17.4, Problem 10E

Chapter 17.4, Problem 12E

Students have asked these similar questions

i need help please

slove the initial-value problem. y'' + 7y' + 12y = 0, y(0) = 2, y'(0) = 8

help on this integral below?

Chapter 17 Solutions

Calculus - Standalone book

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

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

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.

Want to see the full answer?

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 $2 \leq u \leq 2.1, 3 \leq v \leq 3.2$ .