3. Cylindrical and Spherical Coordinates Let E denote the triangular prism with vertices (U, U, U), (a, 0, 0), (0, a, 0), (0,0, a), (a, 0, a), and (0, a, a), where a > 0 is a constant. Compute the volume of E using: (a) Cartesian/rectangular coordinates. (b) Cylindrical coordinates. (c) Spherical coordinates. (You'll need a sum of two iterated integrals here.)
3. Cylindrical and Spherical Coordinates Let E denote the triangular prism with vertices (U, U, U), (a, 0, 0), (0, a, 0), (0,0, a), (a, 0, a), and (0, a, a), where a > 0 is a constant. Compute the volume of E using: (a) Cartesian/rectangular coordinates. (b) Cylindrical coordinates. (c) Spherical coordinates. (You'll need a sum of two iterated integrals here.)
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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Transcribed Image Text:3. Cylindrical and Spherical Coordinates
Let E denote the triangular prism with vertices (U, u, U), (a, 0, 0), (0, a, 0), (0,0, a), (a, 0, a), and
(0, a, a), where a > 0 is a constant. Compute the volume of E using:
(a) Cartesian/rectangular coordinates.
(b) Cylindrical coordinates.
(c) Spherical coordinates. (You'll need a sum of two iterated integrals here.)
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