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Use Stokes' Theorem to evaluate F. dr where F(x, y, z) = (5x + y,3y+ z?,3z + x²) and C is the triangle with vertices (2, 0, 0), (0, 2, 0), and (0, 0, 2) oriented counterclockwise as viewed from above. Since the triangle is oriented counterclockwise as viewed from above the surface we attach to the triangle is oriented upwards curl F = <-2z, -2х, -2y> Σ The easiest surface to attach to this curve is the interior of the triangle. Using this surface in Stokes' Theorem evaluate the following. X2 У2 F. dr = Σdy dx У where Y2 = Σ X1 = Σ X2 = Σ Evaluate F. dr = Σ M M M M

Use Stokes' Theorem to evaluate F. dr where F(x, y, z) = (5x + y,3y+ z?,3z + x²) and C is the triangle with vertices (2, 0, 0), (0, 2, 0), and (0, 0, 2) oriented counterclockwise as viewed from above. Since the triangle is oriented counterclockwise as viewed from above the surface we attach to the triangle is oriented upwards curl F = <-2z, -2х, -2y> Σ The easiest surface to attach to this curve is the interior of the triangle. Using this surface in Stokes' Theorem evaluate the following. X2 У2 F. dr = Σdy dx У where Y2 = Σ X1 = Σ X2 = Σ Evaluate F. dr = Σ M M M M

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.4: Values Of The Trigonometric Functions
Problem 23E
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Use Stokes' Theorem to evaluate F. dr
Transcribed Image Text:Use Stokes' Theorem to evaluate F. dr
where F(x, y, z) = (5x + y,3y+ z?,3z + x²) and C is the triangle with vertices (2, 0, 0), (0, 2, 0), and (0, 0, 2) oriented counterclockwise as viewed from above. Since the triangle is oriented counterclockwise as viewed from above the surface we attach to the triangle is oriented upwards curl F = <-2z, -2х, -2y> Σ The easiest surface to attach to this curve is the interior of the triangle. Using this surface in Stokes' Theorem evaluate the following. X2 У2 F. dr = Σdy dx У where Y2 = Σ X1 = Σ X2 = Σ Evaluate F. dr = Σ M M M M
Transcribed Image Text:where F(x, y, z) = (5x + y,3y+ z?,3z + x²) and C is the triangle with vertices (2, 0, 0), (0, 2, 0), and (0, 0, 2) oriented counterclockwise as viewed from above. Since the triangle is oriented counterclockwise as viewed from above the surface we attach to the triangle is oriented upwards curl F = <-2z, -2х, -2y> Σ The easiest surface to attach to this curve is the interior of the triangle. Using this surface in Stokes' Theorem evaluate the following. X2 У2 F. dr = Σdy dx У where Y2 = Σ X1 = Σ X2 = Σ Evaluate F. dr = Σ M M M M
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