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Calculate / Ss (4xy + e- )dS, where S is the triangle in Figure 1 with vertices (0, 0, 3), (1,0, 2) and (0, 4, 1). (0, 0, 3) (1,0, 2) (0, 4, 1)

Calculate / Ss (4xy + e- )dS, where S is the triangle in Figure 1 with vertices (0, 0, 3), (1,0, 2) and (0, 4, 1). (0, 0, 3) (1,0, 2) (0, 4, 1)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem Statement:** Calculate \(\iint_{S} (4xy + e^z) \, dS\), where \(S\) is the triangle in Figure 1 with vertices \((0, 0, 3)\), \((1, 0, 2)\), and \((0, 4, 1)\). Round your answer to two decimal places. **Diagram Explanation:** The image shows the triangle \(S\) in a 3D coordinate system where: - The x-axis is horizontal. - The y-axis is horizontal (perpendicular to the x-axis). - The z-axis is vertical. The vertices of the triangle \(S\) are labeled as: - \((0, 0, 3)\) - \((1, 0, 2)\) - \((0, 4, 1)\) The triangle is depicted with each vertex connected by straight lines, forming a triangular plane. **Instructions:** Perform a surface integral over the triangle \(S\) defined by these vertices. The integral expression is \(\iint_{S} (4xy + e^z) \, dS\). Evaluate this integral and round the final answer to two decimal places.
Transcribed Image Text:**Problem Statement:** Calculate \(\iint_{S} (4xy + e^z) \, dS\), where \(S\) is the triangle in Figure 1 with vertices \((0, 0, 3)\), \((1, 0, 2)\), and \((0, 4, 1)\). Round your answer to two decimal places. **Diagram Explanation:** The image shows the triangle \(S\) in a 3D coordinate system where: - The x-axis is horizontal. - The y-axis is horizontal (perpendicular to the x-axis). - The z-axis is vertical. The vertices of the triangle \(S\) are labeled as: - \((0, 0, 3)\) - \((1, 0, 2)\) - \((0, 4, 1)\) The triangle is depicted with each vertex connected by straight lines, forming a triangular plane. **Instructions:** Perform a surface integral over the triangle \(S\) defined by these vertices. The integral expression is \(\iint_{S} (4xy + e^z) \, dS\). Evaluate this integral and round the final answer to two decimal places.
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