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#1. S is the part of the plane 5x - 4y + z = 2 that is above 0 ≤ x ≤ 1,0 ≤ y ≤ 1 in the x F = (x, 2y,3z) is a vector field defined on a set containing S. Calculate ff, F.ds

#1. S is the part of the plane 5x - 4y + z = 2 that is above 0 ≤ x ≤ 1,0 ≤ y ≤ 1 in the x F = (x, 2y,3z) is a vector field defined on a set containing S. Calculate ff, F.ds

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem 1:** S is the part of the plane \(5x - 4y + z = 2\) that is above \(0 \leq x \leq 1; 0 \leq y \leq 1\) in the xy-plane. \(F = \langle x, 2y, 3z \rangle\) is a vector field defined on a set containing S. Calculate \(\iint_{S} F \cdot dS\). --- **Explanation of the Diagram:** The diagram includes two points: \((0, \frac{5}{3}, 0)\) and \((0, 0, 2)\). These points are labeled on a sketch of the plane \(5x - 4y + z = 2\), representing specific locations on or above this plane segment in the given region of the xy-plane.
Transcribed Image Text:**Problem 1:** S is the part of the plane \(5x - 4y + z = 2\) that is above \(0 \leq x \leq 1; 0 \leq y \leq 1\) in the xy-plane. \(F = \langle x, 2y, 3z \rangle\) is a vector field defined on a set containing S. Calculate \(\iint_{S} F \cdot dS\). --- **Explanation of the Diagram:** The diagram includes two points: \((0, \frac{5}{3}, 0)\) and \((0, 0, 2)\). These points are labeled on a sketch of the plane \(5x - 4y + z = 2\), representing specific locations on or above this plane segment in the given region of the xy-plane.
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