
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
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, 08:54 AM  #3 
Senior Member Joined: Dec 2015 From: Earth Posts: 153 Thanks: 21 
what does this A mean ?

December 6th, 2015, 11:26 AM  #4 
Newbie Joined: Nov 2015 From: Novosibirsk Posts: 4 Thanks: 0  
December 6th, 2015, 12:24 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 17,524 Thanks: 1318 
Why would one know the values of $x_0,\,x_1$ and $a$ in a typical problem?

December 6th, 2015, 08:25 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 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: 17,524 Thanks: 1318 
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 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Find the length of the parabolic segment r=(3/(1+sin(ø)))  mathdisciple  Calculus  1  April 21st, 2014 09:53 PM 
Circle segment area  Pivskid  Algebra  11  July 3rd, 2013 08:25 AM 
Finding area of shaded segment within a circle.  Tutu  Algebra  3  May 8th, 2012 07:14 AM 
Area of a segment of a circle from % of height.  fishinmyi  Algebra  6  October 27th, 2011 09:34 AM 
Area under a parabolic section (justification)  triplekite  Calculus  1  December 24th, 2010 11:57 PM 