6. Let E be the solid region that is inside both sphere x² + y² + z² = 2 and cylinder x² + y² = 1 and in the first octant. Let the density of the solid at (x, y, z) be p(x, y, z) = x² + y². (a). Sketch the solid region E. (b). Set up iterated integral(s) (DO NOT evaluate) for the mass of E using the rectangular coordinates. (c). Repeat (b) using the cylindrical coordinates.

6. Let E be the solid region that is inside both sphere x² + y² + z² = 2 and cylinder x² + y² = 1 and in the first octant. Let the density of the solid at (x, y, z) be p(x, y, z) = x² + y². (a). Sketch the solid region E. (b). Set up iterated integral(s) (DO NOT evaluate) for the mass of E using the rectangular coordinates. (c). Repeat (b) using the cylindrical coordinates.

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

6. fast please with full steps thank you. please

6. Let E be the solid region that is inside both sphere x² + y² + z² = 2 and cylinder x² + y² = 1 and in the first
octant. Let the density of the solid at (x, y, z) be p(x, y, z) = x² + y².
(a). Sketch the solid region E.
(b). Set up iterated integral(s) (DO NOT evaluate) for the mass of E using the rectangular coordinates.
(c). Repeat (b) using the cylindrical coordinates.
(d). Repeat (b) using the spherical coordinates.
(e). Evaluate ONE of the set ups in (b), (c), and (d).

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