My Math Forum Atanov’s formula for parabolic segment area

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 December 5th, 2015, 10:35 AM #1 Newbie   Joined: Nov 2015 From: Novosibirsk Posts: 4 Thanks: 0 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.
 December 6th, 2015, 06:29 AM #2 Newbie   Joined: Nov 2015 From: Novosibirsk Posts: 4 Thanks: 0 Sorry, I have corrected one error, here is new link.
 December 6th, 2015, 08:54 AM #3 Senior Member   Joined: Dec 2015 From: Earth Posts: 142 Thanks: 20 what does this A mean ?
December 6th, 2015, 11:26 AM   #4
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Quote:
 Originally Posted by idontknow what does this A mean ?
Area of a parabolic segment

 December 6th, 2015, 12:24 PM #5 Global Moderator   Joined: Dec 2006 Posts: 16,954 Thanks: 1256 Why would one know the values of $x_0,\,x_1$ and $a$ in a typical problem?
December 6th, 2015, 08:25 PM   #6
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Quote:
 Originally Posted by skipjack 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.

 December 6th, 2015, 09:49 PM #7 Newbie   Joined: Dec 2015 From: Novosibirsk Posts: 1 Thanks: 0 The formula can be generalized to any parabola ax^2+bx+c=0, where a does not equal 0: A=(|a|(dx)^3)/6
 December 7th, 2015, 11:56 AM #8 Global Moderator   Joined: Dec 2006 Posts: 16,954 Thanks: 1256 Provided that $\Delta x$ is defined in such a way that it is always positive, which wasn't done clearly in the linked proof.

 Tags area, atanov’s, formula, parabola, parabolic, segment

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