Answered: 4. Evaluate ([[. (2x+3y)dxdydz where S…

4. Evaluate ([[. (2x+3y)dxdydz where S is the tetrahedron in the first octant bounded by the coordinate planes and the plane 2x+3y+z = 6 49 а. 3 b. 22 25 с. 2 d. 18 None of these

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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Question

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**Problem Statement:**

Evaluate the triple integral $\iiint_{S} (2x+3y) \, dx \, dy \, dz$ where $S$ is the tetrahedron in the first octant bounded by the coordinate planes and the plane $2x + 3y + z = 6$.

**Options:**

a. $\frac{49}{3}$

b. 22

c. $\frac{25}{2}$

d. 18

e. None of these

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