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5.8 Calculate the volume of the region in 3 which is above the xy-plane, under the parabo- loid z = x² + y², and inside the elliptic cylinder x2/9 + y²/4 = 1. Use elliptical coordinates x= 3r cos 0, y: = 2r sin 0. 11 50

5.8 Calculate the volume of the region in 3 which is above the xy-plane, under the parabo- loid z = x² + y², and inside the elliptic cylinder x2/9 + y²/4 = 1. Use elliptical coordinates x= 3r cos 0, y: = 2r sin 0. 11 50

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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Please answer 5.8
5.8 Calculate the volume of the region in ³ which is above the xy-plane, under the parabo- loid z = x² + y², and inside the elliptic cylinder x2/9 + y²/4 = 1. Use elliptical coordinates x= 3r cos 0, y = 2r sin 0. 5.9 Consider the solid elliptical rod bounded by the xy-plane, the plane z = ax +By+h through the point (0, 0, h) on the positive z-axis, and the elliptical cylinder x²/a² + y²/b² = 1. Show that its volume is nabh (independent of x and B). Hint: Use elliptical coor- dinates x= ar cos 0, y = br sin 0.
Transcribed Image Text:5.8 Calculate the volume of the region in ³ which is above the xy-plane, under the parabo- loid z = x² + y², and inside the elliptic cylinder x2/9 + y²/4 = 1. Use elliptical coordinates x= 3r cos 0, y = 2r sin 0. 5.9 Consider the solid elliptical rod bounded by the xy-plane, the plane z = ax +By+h through the point (0, 0, h) on the positive z-axis, and the elliptical cylinder x²/a² + y²/b² = 1. Show that its volume is nabh (independent of x and B). Hint: Use elliptical coor- dinates x= ar cos 0, y = br sin 0.
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