This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Name:
You have ﬁfteen minutes to complete the quiz. If anything seems unclear,
please ask.
1. Let f (x, y, z ) be a continuous function of three variables. Let R be the
region between the planes x = 0, y = x, z = 0 and z = 1 − y . Write the
integral of f over R in the orders: (a) dzdydx; (b) dydxdz . (2 points each) 2. Let R be the region where z ≥ 0, inside the sphere center the origin and
radius 2 and outside the sphere, center the origin and radius 1. Set up
triple integrals for the volume of f in: (a) cylindrical coordinates; (b)
spherical coordinates. (2 points each)
Use one of your solutions to (a) and (b) to compute the volume of R. (2
points) 1 Solutions
If you have any questions and / or think you’ve spotted a mistake / typo, please
get in touch with me.
1. (a)
1−y 1 1 f (x, y, z )dzdydx.
0 0 x 1 1−z (b)
1−z f (x, y, z )dydxdz.
2. (a)
2π √ 2 x 0 0 4−r 2 2π rdzdrdθ +
0 1 0 0 √ 1
0 √ 4−r 2 rdzdrdθ.
1−r 2 (b)
2π π /2 2 ρ2 sin(φ)dρdφdθ.
0 0 1 The second of these is the easier to compute (although the ﬁrst is possible).
The inner integral computes to
7 sin(φ)
,
3
the middle to 7π
,
3
and the outer to 14π/3, which is thus the volume. 2 ...
View
Full
Document
This note was uploaded on 09/14/2011 for the course MATH 175 taught by Professor Aldroubi during the Spring '08 term at Vanderbilt.
 Spring '08
 ALDROUBI

Click to edit the document details