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#### Concept explainers

**Stokes’ Theorem for evaluating line integrals**

*Evaluate the line integral*

*by evaluating the surface integral in Stokes’ Theorem with an appropriate choice of S. Assume that C has a counterclockwise orientation.*

**13. F** = 〈*x*^{2} – *z*^{2}, *y*, 2*xz*〉; *C* is the boundary of the plane *z* = 4 – *x* – *y* in the first octant.

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# Chapter 14 Solutions

Calculus: Early Transcendentals (2nd Edition)

# Additional Math Textbook Solutions

Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book

Thomas' Calculus: Early Transcendentals (14th Edition)

Precalculus (10th Edition)

Calculus and Its Applications (11th Edition)

Glencoe Math Accelerated, Student Edition

- use Green 's Theorem to evaluate the line integral. Orient the curve counterclockwise unless otherwise indicated. ∮C y2 dx + x2 dy, where C is the boundary of the square that is given by 0 ≤ x ≤ 1, 0 ≤ y ≤ 1
*arrow_forward*Stokes’ Theorem for evaluating surface integrals Evaluate the line integral in Stokes’ Theorem to determine the value of the surface integral ∫∫S (∇ x F) ⋅ n dS. Assume n points in an upward direction. F = ⟨4x, -8z, 4y⟩; S is the part of the paraboloidz = 1 - 2x2 - 3y2 that lies within the paraboloid z = 2x2 + y2 .*arrow_forward*Let F=xi+yj+zk and let f(x,y,z)=x^2e^(y-z). a) Describe a surface S together with orientation so that double integral (F.dS)<0 b) Explain why you cannot find a surface S so that double integral f(x,y,z)dS<0.*arrow_forward* - Stokes’ Theorem for evaluating line integrals Evaluate theline integral ∮C F ⋅ dr by evaluating the surface integral in Stokes’Theorem with an appropriate choice of S. Assume C has a counterclockwiseorientation. F = ⟨y, xz, -y⟩; C is the ellipse x2 + y2/4 = 1 in the plane z = 1.
*arrow_forward*Evaluate the line integral ∮C F ⋅ dr using Stokes’ Theorem. Assume C has counterclockwise orientation. F = ⟨xz, yz, xy⟩; C is the circle x2 + y2 = 4 in the xy-plane.*arrow_forward*Evaluate the surface integral F*n d-sigma where F = -4xyi + 10x^2j - 4xyzk and S is the surface z = xe^y, x is between 0 and 1, y is between 0 and 1, with upwards orientation.*arrow_forward*

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- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning