While I was attempting to prove the area of a circle formula, I ran into a snag. This is the work that I had (note that I am using the area of an infinite amount of triangles within the circle):(adsbygoogle = window.adsbygoogle || []).push({});

a=1/2bh

=1/2br

da=1/2r db

---(splitting the triangle into 2 right triangles produces b=2r*tan([itex]\frac{θ}{2}[/itex]))

=1/2r (2r tan([itex]\frac{dθ}{2}[/itex]))

=r^{2}tan([itex]\frac{dθ}{2}[/itex])

a=r^{2}[itex]\int^{2π}_{0}(tan(\frac{dθ}{2}))[/itex]

I know that the integration will equal π not only due to inspection, but also because I proved it empirically using Excel. If anyone knows how to do this type of integration, if it is possible at all, or if you see any other problems in my work I would appreciate your help.

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# Integration of f(dx)

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