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Evaluating a Line
(a).
(b).
Evaluating a Line Integral for Different Parametrizations In Exercises 1–4, show that the value of
(a).
(b).
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Chapter 15 Solutions
EBK CALCULUS: EARLY TRANSCENDENTAL FUNC
- Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?arrow_forwardFind the surface area of the "Coolio McSchoolio" surface shown below using the formula: SA = integral, integral D, ||ru * rv||dA %3D The parameterization of the surface is: r(u,v) = vector brackets (uv, u + v, u - v) where u^2 + v^2 <= 1 A.) (pi/3)(6squareroot(6) - 8) B.) (pi/3)(6squareroot(6) - 2squareroot(2)) C.) (pi/6)(2squareroot(3) - squareroot(2)) D.) (pi/6)(squareroot(6) - squareroot(2)) E.) (5pi/6)(6 - squareroot(2))arrow_forwardQ1,- A- Locate the centroid (X only) of the shaded area y=12 -3x 3 m Fig. L.A 2 marrow_forward
- Application of Green's theorem Assume that u and v are continuously differentiable functions. Using Green's theorem, prove that SS'S D Ux Vx |u₁|dA= udv, C Wy Vy where D is some domain enclosed by a simple closed curve C with positive orientation.arrow_forwardFind a parametrization of the line in which the planes x - 2y – 4z = 1 and - 2x + 3y + 6z = - 3 intersect. Find the parametrization of the line. Use a point with z= 0 on the line to determine the parametrization. X = y = Z= - oarrow_forwardSketch a surface representing a function f of two variables x and y. Use the sketch to give geometric interpretations of ∂f∂x and ∂f∂y.arrow_forwardIntegrate the function F(x,y,z) = 6z over the portion of the plane x + y +z = 6 that lies above the square OSxS1,0sys 1 in the xy-plane. ..... F(x,y,z) do = S (Type an exact answer, using radicals as needed.) Get more help - Clear all Check answer N 1231 AM 12/1/2021 HP 2159m hp logitecharrow_forwardLet S be the surface parametrized by r (u, v) 0 ≤ ≤ 27. What shape is S? a sphere part of a sphere an ellipsoid a cone the lateral surface of a cylinder a plane a rectangle in R³ a disk in R³ U COS V u sin v 4- - U for (u, v) in the rectangle defined by 0 ≤ u ≤ 2 andarrow_forward(b) Evaluate the line integral Jo dzalong the simple closed contour C shown in the diagram. -2 -1 2j o 1 2arrow_forwardarrow_back_iosarrow_forward_ios
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
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