Triangle ABC has vertices at (3,1) and (6,4).Rotate this triangle 180 degrees about the origin then reflect it over the Y-Axis.
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First, rewrite the equation so that <em>y</em> is a function of <em>x</em> :
(If you were to plot the actual curve, you would have both and
, but one curve is a reflection of the other, so the arc length for 1 ≤ <em>x</em> ≤ 8 would be the same on both curves. It doesn't matter which "half-curve" you choose to work with.)
The arc length is then given by the definite integral,
We have
Then in the integral,
Substitute
This transforms the integral to
and computing it is trivial:
We can simplify this further to
