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Chapter 17 Solutions
Calculus: Early Transcendentals (3rd Edition)
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Calculus & Its Applications (14th Edition)
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- Stokes’ Theorem for evaluating surface integrals Evaluatethe line integral in Stokes’ Theorem to determine the value of thesurface integral ∫∫S (∇ x F) ⋅ n dS. Assume n points in an upwarddirection. F = ⟨2y, -z, x - y - z⟩; S is the cap of the spherex2 + y2 + z2 = 25, for 3 ≤ x ≤ 5 (excluding its base).arrow_forwardStokes’ 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_forwardSurface integrals using an explicit description Evaluate the surface integral ∫∫S ƒ(x, y, z) dS using an explicit representation of the surface. ƒ(x, y, z) = x2 + y2; S is the paraboloid z = x2 + y2, for 0 ≤ z ≤ 1.arrow_forward
- Using Stokes’ Theorem to evaluate a surface integral Evaluate∫∫S (∇ x F) # n dS, where F = -y i + x j + z k, in the following cases.a. S is the part of the paraboloid z = 4 - x2 - 3y2 that lies within the paraboloid z = 3x2 + y2 (the blue surface as shown). Assume n pointsin the upward direction on S.b. S is the part of the paraboloid z = 3x2 + y2 that lies within the paraboloidz = 4 - x2 - 3y2, with n pointing in the upward direction on S.c. S is the surface in part (b), but n pointing in the downward direction on S.arrow_forwardStokes’ 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 = ⟨y, z - x, -y⟩; S is the part of the paraboloidz = 2 - x2 - 2y2 that lies within the cylinder x2 + y2 = 1.arrow_forwardFlux Integral, Evaluate double integral S of sin(y)*cos(z)i +e^x*cos(z)j+cos(y)*ln(1+x^2)k)·NdS, where S is the sphere x^2+y^2+z^2=1 oriented outwards.arrow_forward
- Surface integrals using a parametric description Evaluate the surface integral ∫∫S ƒ dS using a parametric description of the surface. ƒ(x, y, z) = x2 + y2, where S is the hemisphere x2 + y2 + z2 = 36, for z ≥ 0arrow_forwardFind the area of the surface generated revolving the given curve about the y-axis. 1. X=y^3 , 0 is less than equal to Y is less than equal to 1. 2. X=[Y-11], 0 is less than equals to Y is less than equals to 2.arrow_forwardStokes’ Theorem for evaluating surface integrals Evaluatethe line integral in Stokes’ Theorem to determine the value of thesurface integral ∫∫S (∇ x F) ⋅ n dS. Assume n points in an upwarddirection. F = r/ |r|; S is the paraboloid x = 9 - y2 - z2, for 0 ≤ x ≤ 9(excluding its base), and r = ⟨x, y, z⟩ .arrow_forward
- Stokes’ Theorem for evaluating surface integrals Evaluatethe line integral in Stokes’ Theorem to determine the value of thesurface integral ∫∫S (∇ x F) ⋅ n dS. Assume n points in an upwarddirection. F = ⟨x, y, z⟩; S is the upper half of the ellipsoid x2/4 + y2/9 + z2 = 1.arrow_forward6.Finding the Area of a Surface of Revolution. Set up and evaluate the definite integral forthe area of the surface generated by revolving the curve aboutthe y-axis. y=1−x²/4, 0≤x≤2 7.Use Implicit derivatives to find an equation of the tangent line to the curve sinx+cosy=1 at point (?/2,?/2). 5.Find the area of the region bounded by the graphs of x=3−y^2 and x=1+yarrow_forwardUsing cylindrical coordinates evaluate ʃ ʃ ʃE sqrt ((x2 + y2)) dV where E is the solid bounded by the circular paraboloid z = 1 – 16 (x2 + y2) and the xy-plane.arrow_forward
- 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