7. Which of the following statements are true? I. Let R be the region bounded by x + y = 1, x+y = 3₁ y² = x² = 1 and x² - y² = 1. Then - y)e²²-y² dA= -LL- R the substitution u = x - y and v=x+y. II. The volume of the region S that is inside the cylinder x² + y² = a, above the plane z = 0 and below the plane z = 4 - y is 4ña. -2-1 2-z-y III. The integral uv ue" du du for (a) (b) (c) (d) (e) dz dy dr represents the volume of the tetrahedral region bounded by planes z = 0, y = 0, z = 0 and x+y+z=2. IV. The integral p²sinó dp độ dº calculates the volume of the region above the plane z = 0, inside the sphere x² + y² + z² = 4 and outside the sphere x² + y² + (z − 1)² = 1. I only III only I, III II, III I, IV
7. Which of the following statements are true? I. Let R be the region bounded by x + y = 1, x+y = 3₁ y² = x² = 1 and x² - y² = 1. Then - y)e²²-y² dA= -LL- R the substitution u = x - y and v=x+y. II. The volume of the region S that is inside the cylinder x² + y² = a, above the plane z = 0 and below the plane z = 4 - y is 4ña. -2-1 2-z-y III. The integral uv ue" du du for (a) (b) (c) (d) (e) dz dy dr represents the volume of the tetrahedral region bounded by planes z = 0, y = 0, z = 0 and x+y+z=2. IV. The integral p²sinó dp độ dº calculates the volume of the region above the plane z = 0, inside the sphere x² + y² + z² = 4 and outside the sphere x² + y² + (z − 1)² = 1. I only III only I, III II, III I, IV
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:7. Which of the following statements are true?
I. Let R be the region bounded by x + y = 1,
x + y = 3, y² – x² = 1 and x² – y² = 1. Then
-3
dA =
ueu" du dv for
R
the substitution u = x – y and v = x + y.
II. The volume of the region S that is inside the
cylinder a? + y? = a, above the plane z = 0 and
below the plane z = 4 – y is 47a.
2-r-y
I. The integral
dz dy dx
represents the volume of the tetrahedral region
bounded by planes x = 0, y = 0, z = 0 and
x + y+z = 2.
IV. The integral
1ø dp do
de
calculates the volume of the region above the
plane z = 0, inside the sphere r²+ y² + z² = 4
and outside the sphere a² + y² + (z – 1)² = 1.
(a)
I only
(b)
III only
(c)
I, III
(d)
II, III
(e)
I, IV
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