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Solve the problem. Write an iterated triple integral in the order dz dy dx for the volume of the region enclosed by the paraboloids z= 32-x2 - y² and z=x2 + y2. Hint: Graph both in GeoGebra. The projection onto xy plane will be a circle of radius 4 with equation x^2 + y^2 = 16 V32 -x2 32- dz dy dx 32-x² x2• y2 N32-x2 16-x2 - y2 dz dy dx V16-x2 dz dy dx V16-x2 x2• y2 V16-x2 16-x2 - dz dy dx 16-x² x² + y²

Solve the problem. Write an iterated triple integral in the order dz dy dx for the volume of the region enclosed by the paraboloids z= 32-x2 - y² and z=x2 + y2. Hint: Graph both in GeoGebra. The projection onto xy plane will be a circle of radius 4 with equation x^2 + y^2 = 16 V32 -x2 32- dz dy dx 32-x² x2• y2 N32-x2 16-x2 - y2 dz dy dx V16-x2 dz dy dx V16-x2 x2• y2 V16-x2 16-x2 - dz dy dx 16-x² x² + y²

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.CR: Review Exercises
Problem 22CR
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Solve the problem. Write an iterated triple integral in the order dz dy dx for the volume of the region enclosed by the paraboloids z= 32- x2 - y2 and z=x2 + y2. Hint: Graph both in GeoGebra. The projection onto xy plane will be a circle of radius 4 with equation x^2 + y^2 = 16 Z = V32 - x2 32-x2 - y² dz dy dx -V32-x2 x2+y2 4 V32-x2 16-x² - y² dz dy dx -V32-x2 x2 + y2 V16-x2 32-x2 - y² dz dy dx -V16-x2 x2+ y2 4 V16-x2 16-x² - y2 dz dy dx -V16-x2 x2 + y2
Transcribed Image Text:Solve the problem. Write an iterated triple integral in the order dz dy dx for the volume of the region enclosed by the paraboloids z= 32- x2 - y2 and z=x2 + y2. Hint: Graph both in GeoGebra. The projection onto xy plane will be a circle of radius 4 with equation x^2 + y^2 = 16 Z = V32 - x2 32-x2 - y² dz dy dx -V32-x2 x2+y2 4 V32-x2 16-x² - y² dz dy dx -V32-x2 x2 + y2 V16-x2 32-x2 - y² dz dy dx -V16-x2 x2+ y2 4 V16-x2 16-x² - y2 dz dy dx -V16-x2 x2 + y2
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