Find an iterated integral for the surface integral ∬ S f ( x , y , z ) d S where f ( x , y , z ) = x + y and the surface S is given by r( u , v ) = ( u + v )i + ( u − v )j + ( uv )k, 0 ≤ u ≤ 1, 0 ≤ v ≤ 1. a) ∫ 0 1 ∫ 0 1 2 u 2 u 2 + 2 v 2 d u d v b) ∫ 0 1 ∫ 0 1 2 u 2 + 2 v 2 d u d v c) ∫ 0 1 ∫ 0 1 2 u 2 u 2 + 2 v 2 + 4 d u d v d) ∫ 0 1 ∫ 0 1 2 u 2 + 2 v 2 + 4 d u d v

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Study Guide for Stewart's Multivar...

8th Edition
Stewart + 1 other
Publisher: Brooks Cole
ISBN: 9781305271845
BuyFind

Study Guide for Stewart's Multivar...

8th Edition
Stewart + 1 other
Publisher: Brooks Cole
ISBN: 9781305271845

Solutions

Chapter
Section
Chapter 16.7, Problem 1PT
Textbook Problem

Find an iterated integral for the surface integral S f ( x , y , z )   d S where f(x, y, z) = x + y and the surface S is given by r(u, v) = (u + v)i + (uv)j + (uv)k, 0 ≤ u ≤ 1, 0 ≤ v ≤ 1.

  1. a) 0 1 0 1 2 u 2 u 2 + 2 v 2   d u   d v
  2. b) 0 1 0 1 2 u 2 + 2 v 2   d u   d v
  3. c) 0 1 0 1 2 u 2 u 2 + 2 v 2 + 4   d u   d v
  4. d) 0 1 0 1 2 u 2 + 2 v 2 + 4   d u   d v

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Chapter 16 Solutions

Study Guide for Stewart's Multivariable Calculus, 8th
Ch. 16.3 - Which curve is simple but not closed?Ch. 16.3 - True or False: F(x,y)=(x2+2y2)i+(y2+2x2)j is...Ch. 16.3 - True or False: Let F(x, y) = 2x cos yi x2 sin yj...Ch. 16.3 - Let C be the line from (1, 0) to (0, 1) and F(x,...Ch. 16.4 - True or False: Suppose C in the figure at the...Ch. 16.4 - If D is a region enclosed by a closed curve C,...Ch. 16.4 - Let C be the curve that bounds the rectangle at...Ch. 16.4 - The area of a region D enclosed by a curve C, such...Ch. 16.5 - Find the curl of F(x, y, z) = (x2 + y2)i + (xz)j +...Ch. 16.5 - True or False: If F is conservative, then curl F =...Ch. 16.5 - Find div F for F(x, y, z) = (x2 + y2)i + (xz)j +...Ch. 16.5 - True or False: div curl F = 0.Ch. 16.5 - One of the vector forms of Greens Theorem says...Ch. 16.5 - One of the vector forms of Greens Theorem says...Ch. 16.6 - A parametrization of the cylinder in the figure...Ch. 16.6 - Find the normal vector to the tangent plane at the...Ch. 16.6 - The equation of the tangent plane corresponding to...Ch. 16.6 - A surface S is parameterized by x = sin u, y = sin...Ch. 16.6 - Write an iterated integral for the area of that...Ch. 16.7 - Find an iterated integral for the surface integral...Ch. 16.7 - Find an iterated integral for SFdS where S is the...Ch. 16.7 - Let F(x, y, z) = (2x + 3y + z)i + (z 2y)j + (x +...Ch. 16.8 - Let F(x, y, z) = Pi + Qj + Rk have continuous...Ch. 16.8 - Let F(x, y, z) = zi xj + yk, let C be the circle...Ch. 16.8 - Let F(x, y, z) = zi + xj yk and the curve C be...Ch. 16.9 - Let F(x, y, z) = Pi + Qj + Rk have continuous...Ch. 16.9 - Let S be the surface of the closed cylindrical...

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