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I was reading this thread:

Is this Batman equation for real?

and I wondered if the area bounded by the curve had a nice closed form.

The resulting integrals were slightly beyond me, so I thought I would ask you guys for help. Perhaps complex analysis will be useful.

Community
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user85798
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  • Straight lines and arcs of circles, ellipses and parabolas with simple end points mean that the area can be calculated in a closed form. But there is no reason to suppose it is particularly "nice". – Henry May 12 '14 at 22:13

1 Answers1

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http://www.wolframalpha.com/input/?i=batman+equation

If you go down to the section labelled area, they have the simplest form of the area of it.

$$\text{Area} = \frac{955}{48}-\frac{2}{7} (-3 \sqrt{10}+2 \sqrt{33}+7 \pi+3 \sqrt{10} \pi)+21 \cos^{-1}\left(\frac{3}{7}\right)+21 \cos^{-1}\left(\frac{4}{7}\right)$$

Hakim
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Asimov
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