Let D be the region in space enclosed by z =-2x2 - y2 and z = -12 +x2 + 2y2. Our aim is to find the volume of D using triple integral in Cartesian coordinates. By using the order dzdxdy, the limits of integration of z are: -12 + x? + 2y? SzS-2x? - y? -2x2 - y

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 40E: Find the exact volume of the solid that results when the region bounded in quadrant I by the axes...
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Quest 7
Let D be the region in space enclosed by z = -2x² - y2 and
z = -12 + x2 + 2y². Our aim is to find the volume of D using triple
integral in Cartesian coordinates. By using the order dzdxdy, the limits
of integration of z are:
-12 + x? + 2y?sz5-2x? - y²
-2x2 – y? < z <-12+ x² + 2y2
as above
as above.
None of these
O Oszs12
0 Sz< 12 – x² – 2y2
Transcribed Image Text:Let D be the region in space enclosed by z = -2x² - y2 and z = -12 + x2 + 2y². Our aim is to find the volume of D using triple integral in Cartesian coordinates. By using the order dzdxdy, the limits of integration of z are: -12 + x? + 2y?sz5-2x? - y² -2x2 – y? < z <-12+ x² + 2y2 as above as above. None of these O Oszs12 0 Sz< 12 – x² – 2y2
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