The volume V of the solid having the shape of the region in the first octant (x ≥ 0, y ≥0, z≥ 0) enclosed by the surfaces y = 4 - x² and z = 7+ 3y² is given by which of the following? 2 4-x²2² (6²6 00 0 (i) V= (iii) V = - (v) V= Lo C 2 2 S 00 4-x2 (v) & (vi) ○ (i) & (ii) ○ (i) & (v) O (ii) & (vi) Only (vi) Only (ii) -20 (iii) & (iv) +3y2² dz dy dx (ii) V = 0 (7+3y²) dy dx (vi) ² sª 00 0 [VA-Y 0 ¶¯ (7 + 3y²) dz dy dx__(iv) V = S s 0 0 dz dy dx (7 + 3y²) dx dy 7+3y² dx dy

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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The volume V of the solid having the shape of the region in the first octant
(x ≥ 0, y ≥0, z≥ 0) enclosed by the surfaces y = 4 - x² and z = 7+ 3y²
is given by which of the following?
4-x²2²
-1²-²7-²
s
0 0
0
(i) V=
2
2 4-x2
(i) = √² ²²² ²
00
(v) V =
2
-2 0
(v) & (vi)
(i) & (ii)
(i) & (v)
(ii) & (vi)
Only (vi)
Only (ii)
(iii) & (iv)
dz dy dx
(ii) V =
(7+3y²) dy dx (vi)
(7+3y²) dz dy dx (iv) V=
C
*
00
0
0
dz dy dx
y
(7 + 3y²) dx dy
.7+ 3y²
0
dx dy
Transcribed Image Text:The volume V of the solid having the shape of the region in the first octant (x ≥ 0, y ≥0, z≥ 0) enclosed by the surfaces y = 4 - x² and z = 7+ 3y² is given by which of the following? 4-x²2² -1²-²7-² s 0 0 0 (i) V= 2 2 4-x2 (i) = √² ²²² ² 00 (v) V = 2 -2 0 (v) & (vi) (i) & (ii) (i) & (v) (ii) & (vi) Only (vi) Only (ii) (iii) & (iv) dz dy dx (ii) V = (7+3y²) dy dx (vi) (7+3y²) dz dy dx (iv) V= C * 00 0 0 dz dy dx y (7 + 3y²) dx dy .7+ 3y² 0 dx dy
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