4. Let D be the region in the first octant bounded by the coordinate planes, the plane x + z = 1 and the cylinder x = 1-y². Which of the integrals below are equivalent to the integral [[[√²³ x² + y² + ²² dV ? e D 1-y² I. I ez²+²+² dz dx dy 0 II. 11. LL²+²+² dy de dz 70 pl P√z pl-z e

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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4. Let D be the region in the first octant bounded by
the coordinate planes, the plane x + z = 1 and
the cylinder r = 1-y² . Which of the integrals below
+y²+²²&V ?
are equivalent to the integral
I.
dz dx dy
1
1-z
-1-r
22+y²+z²
dy dæ dz
II.
1-z
III.
CE?+y²+z² dx dy dz +
LLL"-
1-y?
ez²+y²+z² dx dy dz
(a)
I only
(b)
II only
(c)
III only
(d) I, II
(e)
I, III
Transcribed Image Text:4. Let D be the region in the first octant bounded by the coordinate planes, the plane x + z = 1 and the cylinder r = 1-y² . Which of the integrals below +y²+²²&V ? are equivalent to the integral I. dz dx dy 1 1-z -1-r 22+y²+z² dy dæ dz II. 1-z III. CE?+y²+z² dx dy dz + LLL"- 1-y? ez²+y²+z² dx dy dz (a) I only (b) II only (c) III only (d) I, II (e) I, III
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