Surface
36. f(x, y, z)=x2+y2; S is the paraboloid z=x2 + y2. for 0 ≤ z ≤ 1.
Trending nowThis is a popular solution!
Chapter 17 Solutions
Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
Calculus & Its Applications (14th Edition)
University Calculus: Early Transcendentals (3rd Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Glencoe Math Accelerated, Student Edition
Precalculus Enhanced with Graphing Utilities (7th Edition)
- Evaluate the integral: I = ∭s 2x dxdydz where the solid S is defined as: S = { (x, y, z) ∈ R3 : x ≥ 0 ; 0 ≤ y ≤ 2z + 1 ; x2 + y2 + 4z2 ≤ 1 } (a) Describe or sketch the solid S. (b) Evaluate the integral using the shadow method. Show all the workings and explain the methods used.arrow_forwardEvaluate 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_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 = ⟨2y, -z, x - y - z⟩; S is the cap of the spherex2 + y2 + z2 = 25, for 3 ≤ x ≤ 5 (excluding its base).arrow_forward
- Find the area of the surface given by z = f(x,y) over the region R. R: The triangle with vertices (0,0), (2,0), and (0,2) f(x,y) = 2x + 2y Answer: 6 (but how do I get there?)arrow_forwardLet 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_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
- 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 = r/ |r|; S is the paraboloid x = 9 - y2 - z2, for 0 ≤ x ≤ 9(excluding its base), and r = ⟨x, y, z⟩ .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_forwardLet S be the solid of revolution obtained by revolving about the x-axis the bounded region R enclosed by the curve y=e−2x and the lines x=−1, x=1 and y=0. We compute the volume of S using the disk method. a) Let u be a real number in the interval −1≤x≤1. The section x=u of S is a disk. What is the radius and area of the disk? Radius: Area: b) The volume of S is given by the integral (b to a) ∫f(x)dx, where: a= b= and f(x)= c) Find the volume of S. Give your answer with an accuracy of four decimal places. Volume:arrow_forward
- Find the volume of the solid of revolution generated when the area described is rotated about the x-axis.a.) The area between the curve y = x and the ordinates x = 0 and x =4 b.) The area between the curve y = x3/2 and the ordinates x = 1 and x = 3 c.) The area between the curve x2 + y2 + 16 and the ordinates x = -1 and x = 1arrow_forwardNot using divergence theorem. I just need I don't need to solve. Just need the surface integral for S1 and S2arrow_forwardChoosing a more convenient surface The goal is to evaluateA = ∫∫S (∇ x F) ⋅ n dS, where F = ⟨yz, -xz, xy⟩ and S is thesurface of the upper half of the ellipsoid x2 + y2 + 8z2 = 1 (z ≥ 0).a. Evaluate a surface integral over a more convenient surface to find the value of A.b. Evaluate A using a line integral.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