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December 5th, 2015, 09:35 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, 07:54 AM  #3 
Senior Member Joined: Dec 2015 From: Earth Posts: 226 Thanks: 26 
what does this A mean ?

December 6th, 2015, 10:26 AM  #4 
Newbie Joined: Nov 2015 From: Novosibirsk Posts: 4 Thanks: 0  
December 6th, 2015, 11:24 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 19,057 Thanks: 1618 
Why would one know the values of $x_0,\,x_1$ and $a$ in a typical problem?

December 6th, 2015, 07:25 PM  #6 
Newbie Joined: Nov 2015 From: Novosibirsk Posts: 4 Thanks: 0  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 07:52 PM. 
December 6th, 2015, 08:49 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, 10:56 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 19,057 Thanks: 1618 
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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