Let D be the tetrahedron in the first octant bounded by the coordinate planes and the plane 6x + 3y + 2z = 6. a. Use an iterated triple integral to determine the volume of this tetrahedron. b. Set up two of the other five possible iterated triple integrals for this volume. Collectively, you want your three iterate triple integrals to include dV expressions that include one of dxdydz or dxdzdy, one of dydzdx or dydxdz, and one of dzdydx or dzdxdy.
Let D be the tetrahedron in the first octant bounded by the coordinate planes and the plane 6x + 3y + 2z = 6. a. Use an iterated triple integral to determine the volume of this tetrahedron. b. Set up two of the other five possible iterated triple integrals for this volume. Collectively, you want your three iterate triple integrals to include dV expressions that include one of dxdydz or dxdzdy, one of dydzdx or dydxdz, and one of dzdydx or dzdxdy.
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
Let D be the tetrahedron in the first octant bounded by the coordinate planes and the plane
6x + 3y + 2z = 6.
a. Use an iterated triple
b. Set up two of the other five possible iterated triple integrals for this volume. Collectively,
you want your three iterate triple integrals to include dV expressions that include one of
dxdydz or dxdzdy, one of dydzdx or dydxdz, and one of dzdydx or dzdxdy.
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