8. Compute the volume V of the solid region below the surface z = 2xy + 3x² and above the triangle with vertices at the points (0, 0, 0), (0, 1, 0) and (1, 1,0) on the x, y plane. → (A) V = (B) V = (C) V = (D) (E) V = V = 3 1 3 3 4 4 113 2 3 Solution. Let D = {(x, y), 0≤ y ≤ 1,0 ≤ x ≤y}. Then, LL [² 2xy + 3₂², 0 0 V = J₂ D 2xy +3x² dA: -1 = [ ₁² [2 ² y + 2²³²] = = dy = f₁" 2 y ³ dy = 1 4 y dx dy 2 0 = 1
8. Compute the volume V of the solid region below the surface z = 2xy + 3x² and above the triangle with vertices at the points (0, 0, 0), (0, 1, 0) and (1, 1,0) on the x, y plane. → (A) V = (B) V = (C) V = (D) (E) V = V = 3 1 3 3 4 4 113 2 3 Solution. Let D = {(x, y), 0≤ y ≤ 1,0 ≤ x ≤y}. Then, LL [² 2xy + 3₂², 0 0 V = J₂ D 2xy +3x² dA: -1 = [ ₁² [2 ² y + 2²³²] = = dy = f₁" 2 y ³ dy = 1 4 y dx dy 2 0 = 1
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
Section10.6: The Three-dimensional Coordinate System
Problem 40E: For the sphers x-12+y+22+z-42=36 and x2+y2+z2=64, find the ratio of their a surface areas. b...
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![8.
Compute the volume V of the solid region below the surface z = 2xy +3x² and above
the triangle with vertices at the points (0, 0, 0), (0, 1, 0) and (1, 1, 0) on the x, y plane.
→ (A) V
(B) V =
(C) V
(D) V
(E)
=
V
=
||
=
312
3
414 416
1
Solution. Let D = {(x, y), 0 ≤ y ≤ 1, 0≤x≤ y}. Then,
1
V= /[ 2xy +32²dA= [[ 2xy +3a²dr dy
= 6²
1
= [₁²₁ [2² y + 2²³¹] dy =
| 2y³ dy = [4] = ²
0
ال](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca6b5de9-d666-4be4-bec5-372f49facd74%2F33e42651-5c2a-40ff-bc61-2ea360200867%2Fwl0prle_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8.
Compute the volume V of the solid region below the surface z = 2xy +3x² and above
the triangle with vertices at the points (0, 0, 0), (0, 1, 0) and (1, 1, 0) on the x, y plane.
→ (A) V
(B) V =
(C) V
(D) V
(E)
=
V
=
||
=
312
3
414 416
1
Solution. Let D = {(x, y), 0 ≤ y ≤ 1, 0≤x≤ y}. Then,
1
V= /[ 2xy +32²dA= [[ 2xy +3a²dr dy
= 6²
1
= [₁²₁ [2² y + 2²³¹] dy =
| 2y³ dy = [4] = ²
0
ال
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