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2
2005 Calculus #2: Parameterized Stuff - find the length
2005 Calculus #2: Parameterized Stuff - find the length
Source:
April 29, 2013
calculus
integration
trigonometry
logarithms
Problem Statement
A plane curve is parameterized by
x
(
t
)
=
∫
t
∞
cos
u
u
d
u
x(t)=\displaystyle\int_{t}^{\infty} \dfrac {\cos u}{u} \, \mathrm{d}u
x
(
t
)
=
∫
t
∞
u
cos
u
d
u
and
y
(
t
)
=
∫
t
∞
sin
u
u
d
u
y(t) = \displaystyle\int_{t}^{\infty} \dfrac {\sin u}{u} \, \mathrm{d}u
y
(
t
)
=
∫
t
∞
u
sin
u
d
u
for
1
≤
t
≤
2
1 \le t \le 2
1
≤
t
≤
2
. What is the length of the curve?
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