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Unformatted text preview: Version 004/AAABA — DGQch “1 Gilbert m (78759) 1 This print—out shoulé have 3 questions.
Multiplewchoéce questions may continue on
the next column or page  ﬁnd all choices
before answering. 1 2 3 4 5 6
as
an
m 001 10.0 points
Evaluate the triple integral Jeff/£33mng over the points (3:, y, z) in the rectangular box
B m [0,2] X [2, 3] X [0, 1}. 1. I 2 2 correct 2.I r: 1 5
3.1 — é
4.I = 3 3
5. I —— E
Explanation: Since B consists of all points (at, y, 2) such
that 03,231, was; 23;:53, I can be written as a repeated integra} I =/01(/:(/023mz2dm)dy)az. Now 2 2
/ 311222053: 2 [gmgzz] = 622,
0 2 {3 While /: 622dy : [@232]: = 622. In this case, Consequently, 002 10.9 90133133
The solid E shown in x is bounded by the graphs of 2 z=l—$, m+ym1, and the coordinate planes :9, y, z = 0. Write
the tripie integral I: ff/Eﬂagyﬂdlf as a repeated integrai, integrating ﬁrst with
reSpect to 2, then 1 , and finally :3. 1. (fol—$2 f(a:,y,z)dz)dy)dm "x Version_004/AAABA m Doom: " Gilbert — (78759) 2 ' 2. few/1‘0 (/01fo f(:1:, y3 z) dz)dy)dm ‘ 6' I : Mel's “1.). Mm Explanation:
In Cartesian coordinates the region of into 1 1mm2 1wy . .
3° / (f ( ' f($;y,z)dz)dy)dm gratioms I
O 0 {3
2 {Law:Ogygx/mﬁcz’ogmgtl}? l 1—$ lmx
4' f0 (/0 (f0 We 9’ ’3) dz) ‘1de53 V which is the shaded region in correct Explanation: Because E is bounded by the coordinate
planes 3, y, z m 0, the graph of the soiid
shows that E consists of all points (as, y, z) in
3—space satisfying both the inequalities $?yﬂz 2 0} as weil as 0 S 2 S 1~$23 g gig 1mm: 0 S m S I. The graphic shows teat in poiar coordinates
 the region of integration 18 Consequently, as a repeated integral, 1 l~m l—$2
' I. I _:. f0 (f0 [G _ ft”, 9? 3) d3) d9) 0:53 Thus in polar coordinates
' __ : _ ' 4 ﬂ/Q 2  I = f f 231* macaw
keywords: clicker ‘ 0 0 2 1 . 16
n/ re?" ctr m ~7r/ ends,
0 3 0 . setting a 2 r2. Consequently, {(r,9):0£r§4,059§n/2}. 003 10.0 points Evaluate the iterated integrai 4 V16me 2 2
I 2 f f 23‘” +9 dyda:
0 0 by converting to polar coordinates. E I :3 27r(616 1) 1 .
iﬂem —— 1) correct 2. I m %w(e’1~l) 1.1 EE 3. I = 27T(816m 1)‘
4. I m 77(64— 1) 5. I =. 27r(e4 — 1) ...
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 Fall '09
 Gilbert
 Spherical coordinate system, Polar coordinate system, )dM

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