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December 5th, 2015, 10:35 AM   #1
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Atanov’s formula for parabolic segment area

I would like to popularize one interesting formula I have discovered in 2005 during my study at high school. It can be very useful for students for solving a typical problem of finding the area of parabolic segment. I suspect that I'm not the first person, who has discovered the formula, as it is pretty easy to discover it. But in order to facilitate the popularization I had to name it by my surname. So, the formula can be seen on the figure below. The proof is given by this link.

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December 6th, 2015, 06:29 AM   #2
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Sorry, I have corrected one error, here is new link.
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December 6th, 2015, 08:54 AM   #3
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what does this A mean ?
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December 6th, 2015, 11:26 AM   #4
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Quote:
Originally Posted by idontknow View Post
what does this A mean ?
Area of a parabolic segment
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December 6th, 2015, 12:24 PM   #5
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Why would one know the values of $x_0,\,x_1$ and $a$ in a typical problem?
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December 6th, 2015, 08:25 PM   #6
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Quote:
Originally Posted by skipjack View Post
Why would one know the values of $x_0,\,x_1$ and $a$ in a typical problem?
Standard approach for finding the area implies integration from $x_0$ to $x_1$. This formula allows to skip the integration.

Last edited by capslocky; December 6th, 2015 at 08:52 PM.
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December 6th, 2015, 09:49 PM   #7
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The formula can be generalized to any parabola ax^2+bx+c=0, where a does not equal 0: A=(|a|(dx)^3)/6
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December 7th, 2015, 11:56 AM   #8
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Provided that $\Delta x$ is defined in such a way that it is always positive, which wasn't done clearly in the linked proof.
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