1. (10 pts) Suppose a Wire is wound along a cone in such a way that its
path is described by
77(16): (t2,tcost,tsint>, 1 < t < 4
If the Charge density (per unit length) along the Wire is given by
y2+z2
pt’ww): ﬂ ,
find the total Charge in the Wire.
WW “

1. (10 points) Compute the following, in any way you like. (Hint: Draw a
picture!)
\/§ m g «4:;
/ / 3,12 dy dx + / /
' 7
9/1 ”2/ f ‘
\ ’1‘ 5 W 43 an 5);];
1‘ 51mm; m.
k it” ‘ 3 ‘ I ‘
C29 «m
y2dydm+f / y dydm
_\/§ -—:1;
\1r
k
fry/)1 /7(Qﬂ/g(~/:W/Jxﬂ/ﬂ

1. (10 points) Consider the curve C parametrized by
rot):(t~2)i+(t2—5)j+m/t—1k, 23t<5.
Compute the line integral / F - dr Where
C
1+ :32, zsin(yz) + 2xy,1n(1 + £132) + ysin(yz)>.
5 w,
F(w,y,z) = <y2 +
k W,
/ \ ' I , /
I x I x V 2/ l V LY /,yr17)/Tf* ,_

W. Conley
Math 32B, Lecture 3
Fri, Apr 25, 2014
Midterm 1
Last Name:
First Name:
Student ID:
Signature:
Section:
Tuesday:
Thursday:
3A
3B
TA: Ioannis Lagkas-Nikolos
3C
3D
TA: Fei Xie
3E
3F
TA: Sangchul Lee
Instructions: Do not open this exam until instruc

6m
and 0 S :1: S Electric charge has accumulated on this surface so that
TM, A urns/1&5,
. E
1. (10 pomts) Lets:F 8 be the part of the cone x = 2x/y2 + 22 Where g 2 0
\ , ; j,
5 a /‘ y
2n"
at
ta
/
its charge density (per unit area) at each point is
What

TWO PRACTICE MIDTERMS
MATT
1. Practice Midterm 1
Problem 1. Find the area enclosed between the curves y = x2 and y = x2/3 .
Problem 2. Evaluate
y = x.
RR
D (x + y
4 )dA
where D is bounded by y =
5
x and
R 2 R lnx 1
Problem 3. We want to compute 1 0 x(y+1)