Name: _______________________________
Quiz 3 – Keys
1.
What is the length of the curve defined by
3/2
y
x
=
from
0
x
=
to
5
x
=
. Be sure to completely integrate for
the length and provide a numerical answer.
This problem should not be difficult.
1/2
3/2
3
2
dy
x
y
x
dx
=
⇒
=
Just use the length integral:
5
0
9
1
4
x
L
dx
=
+
∫
and you better know how to finish the integration!
2.
What is the length of the curve defined by
ln(sec
)
y
x
=
from
0
x
=
to
4
x
π
=
. Be sure to completely
integrate for the length and provide a numerical answer.
This problem would give everyone a quick refresher
on basic trig identities and trig integrals. We will again meet them soon!
sec
tan
ln(sec
)
tan
sec
dy
x
x
y
x
x
dx
x
=
⇒
=
/4
2
0
1
tan
L
x dx
π
=
+
∫
If you remember the identity:
2
2
sec
1
tan
x
x
=
+
you can use it to finish the integration.

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