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Unformatted text preview: MATH 2340 Multiple Integration and Vector Calculus
Section 67 Midterm Exam 2 May 15, 2007 N :2. E I i _‘. ame: ;  *
Dela ﬁgmg Instructions: 1. Print your name on each page.
2. Show all your work neatly for full credit.
3. No calculators, notes, or books are allowed. 1) Find the moment of intertia Iz (calculated about the 2 M axis) of a uniform sphere of radius R z 5 and unit
volume—mass—density pH") 2 1. ( 16 points) :5; =1 l W W254 «ﬁg/W“ “Fm l I} \ m x?“ M . g : , i
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Nam ) Find the surface area. of the part of the paraboloid z m 10 — m2 — y2 that lies between the two planes 2 : 1 and 2
z:
18 Name: Jg {hﬁfgggﬂ 3) Find the divergence and curl of the vector ﬁeld 1312:, y, z) m (way); + (2 sin + (myln (Show your work) (16 points) a: A: ’m “W ‘
vs 2::— Qik )6“ 3.3:; .1. 3% ﬂ 26mm;
&3C (91’,
M3 “3 A
Va, 1: m 3% s, 3% {26%
3.. 4) Find the area of the ﬁrst quadrant region bounded by the curves 3; 2 m , (18 points) Jﬂiak 1 (is/gadgj’ik 6231!}; cum "; z E *4 z:
a a?) [UL {0'3} 2 y : 23:2, and x : 312,51: : 4y2. x it; L w L)... 2.;
‘T “w? "L 63131)} ‘g‘év “F36” 4 1
s 4 ﬂ
“3. a“. '——. _ ’43.... cﬁmoﬂﬁr ggﬂijQQ/‘m g I ﬂing» 3mg“ ‘* X] 3,me i :3.
4 1,. 4 I
.2 km: :3» 5,, :«Lwr
A HEW/13 egw‘ow 6mm Name‘ gdﬂgmg 5) First determine Whether the vector ﬁeld F (32,31, 2) z (1 + yew); + (2y 4— we“) is conservative ( showing your work). Then, if it is conservative, ﬁnd a potential function for the ﬁeid (16 points) “3 , e .i
ﬁx F : ﬁ [ghyaéh (5%
1?: ,_ if 23$ Lenwvaﬁim
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be gﬁwg): 31,4314» ax? + $sz 6) Evaiuate the line integral [IEd?
C along the curve C, where 15(33, y, z) = 2;} +  y}; and C is parametrized by :1: m t, y : 152, z = t3, 0 S t g 1.
{16 points) . F ~ ;
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This note was uploaded on 09/29/2008 for the course MATH 234 taught by Professor Boeri during the Spring '08 term at Northwestern.
 Spring '08
 Boeri
 Multivariable Calculus

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