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Phys 208 – Test 3 – April 9, 2007
1.(20 pts)
Given the integral
2
()
dt
at
a
π
∞
−∞
=
+
∫
, determine the integral
23
(4
)
dt
t
∞
−∞
+
∫
.
Hint: differentiate a few times with respect to
a
and then set
a
= 4.
2. (20 pts)
In the integral
1
2
00
x
xy
I
ed
yd
x
x
+
+
⎡⎤
=
⎢⎥
⎣⎦
∫∫
, make the change of variables
y
u
x
=
and
vxy
=+
.
a)
Determine the Jacobian
J
for the area so that

dxdy
J dudv
=
.
b)
Determine the new limits and evaluate the integral.
3.(20 pts)
The force acting on a particle of charge
q
and mass
m
moving in a magnetic field
B
G
with a velocity
v
G
is given by
dv
Fq
vB m
dt
=×
=
G
GG
G
.
Assume the magnetic field is in the
z

direction and the motion of the particle is in the
xy
plane.
a)
Show that the magnitude of the velocity is a constant.
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This note was uploaded on 01/08/2011 for the course PHYS 208 taught by Professor J.peat during the Spring '10 term at Missouri S&T.
 Spring '10
 J.Peat

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