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1. Use triple integral to find the volume of the solid in the first octant bounded by the plane 2x+3y+6z = 12 and the coordinate planes. (0, 0, 2) (0, 4, 0) y 2x + 3y + 6z = 12 * (6, 0, 0)

1. Use triple integral to find the volume of the solid in the first octant bounded by the plane 2x+3y+6z = 12 and the coordinate planes. (0, 0, 2) (0, 4, 0) y 2x + 3y + 6z = 12 * (6, 0, 0)

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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### Volume Calculation Using Triple Integrals **Problem Statement:** 1. Use triple integral to find the volume of the solid in the first octant bounded by the plane \(2x + 3y + 6z = 12\) and the coordinate planes. **Diagram Explanation:** - The diagram illustrates a triangular solid in the first octant. - The plane is defined by the equation \(2x + 3y + 6z = 12\). - The solid is bounded by this plane and the coordinate planes (\(xy\), \(yz\), and \(zx\) planes). - The intercepts with the axes are shown: - \(x\)-intercept at \((6, 0, 0)\), - \(y\)-intercept at \((0, 4, 0)\), - \(z\)-intercept at \((0, 0, 2)\). This setup suggests using a triple integral over the region defined by these bounds to calculate the volume.
Transcribed Image Text:### Volume Calculation Using Triple Integrals **Problem Statement:** 1. Use triple integral to find the volume of the solid in the first octant bounded by the plane \(2x + 3y + 6z = 12\) and the coordinate planes. **Diagram Explanation:** - The diagram illustrates a triangular solid in the first octant. - The plane is defined by the equation \(2x + 3y + 6z = 12\). - The solid is bounded by this plane and the coordinate planes (\(xy\), \(yz\), and \(zx\) planes). - The intercepts with the axes are shown: - \(x\)-intercept at \((6, 0, 0)\), - \(y\)-intercept at \((0, 4, 0)\), - \(z\)-intercept at \((0, 0, 2)\). This setup suggests using a triple integral over the region defined by these bounds to calculate the volume.
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