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March 19th, 2011, 11:09 PM   #1
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set up integral problem

The problem is attachment below, you can see it by click on it. This is tricky problem, I need your help, I actually gave up on it , if you know how to solve for it, please help me, thank you so much.
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 March 20th, 2011, 06:00 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: set up integral problem One expression we can use to find c is: $\int_0\,^c \sqrt{r^2-x^2}\,dx=\frac{\pi r^2}{12}$ Using a trigonometric substitution, we find: $$x\sqrt{r^2-x^2}+r^2\sin^{-1}$$\frac{x}{r}$$$_0^c=\frac{\pi r^2}{6}$ $c\sqrt{r^2-c^2}+r^2\sin^{-1}$$\frac{c}{r}$$=\frac{\pi r^2}{6}$ Using a numeric solver with r = 10, we find: $c\approx2.64932084602776862435$
 March 25th, 2011, 07:48 PM #3 Member   Joined: Aug 2009 Posts: 41 Thanks: 0 Re: set up integral problem thank you so much !!!
 March 25th, 2011, 07:54 PM #4 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: set up integral problem I laughed trying to picture a hopped-up Charlie Sheen and "friends" using calculus to cut their pizza!

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