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Mathematics
Problem
Explain why the integrand in the arc-length formula for an even differentiable function
f
f
f
defined on
[
−
a
,
a
]
[-a,a]
[
−
a
,
a
]
is itself an even function, and consequently why the total arc length on
[
−
a
,
a
]
[-a,a]
[
−
a
,
a
]
equals twice the arc length on
[
0
,
a
]
[0,a]
[
0
,
a
]
.
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