My Math Forum Intuitive understanding of how slope is the inverse of area under the curve

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 May 6th, 2017, 05:13 PM #1 Newbie   Joined: Apr 2017 From: USA Posts: 11 Thanks: 0 Intuitive understanding of how slope is the inverse of area under the curve Hello, I'm trying to gain an intuitive understanding regarding how the area under a function is the opposite/inverse of the slope of that function. I am familiar with the ideas that differentiating a function determines the slope and integrating a function determines the area under the function and also the processes most commonly used (ie letting the change in x become infinitely small) to explain the math. However, I'm hoping to obtain a clearer conceptualization of how those two processes are related or why slope really has anything to do with area. I'd appreciate it if someone could explain that concept or point me to a good explanation. Thanks
 May 6th, 2017, 05:48 PM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,805 Thanks: 1449 pretty good intuitive explanation ... integration as the inverse of differentiation Thanks from JeffM1
 May 6th, 2017, 06:20 PM #3 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,749 Thanks: 613 Math Focus: Yet to find out. Also this. Thanks from JeffM1
May 11th, 2017, 05:45 PM   #4
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Thanks for the great responses.

Quote:
 Originally Posted by skeeter pretty good intuitive explanation ... integration as the inverse of differentiation
This is a great explanation and gave me a much better understanding of how differentiation and integration are related.

Quote:
 Originally Posted by Joppy Also this.
Many many thanks for posting this link. It's a super description of what I was after but of much greater significance I believe, is that it introduced me to the series of 3blue1brown math videos.

I've watched a lot of videos in the past because I am a very visual learner but I've never seen any that comes even close to this. The script and audio are exceptional but the visual presentation is incredible.

I was thrilled when Sal Khan took math instruction outside of the lecture hall but I will never again be content with handwritten content now that I know about 3blue1brown.

May 11th, 2017, 05:49 PM   #5
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From: Australia

Posts: 1,749
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Math Focus: Yet to find out.
Quote:
 Originally Posted by WeThotUWasAToad Many many thanks for posting this link. It's a super description of what I was after but of much greater significance I believe, is that it introduced me to the series of 3blue1brown math videos. I've watched a lot of videos in the past because I am a very visual learner but I've never seen any that comes even close to this. The script and audio are exceptional but the visual presentation is incredible. I was thrilled when Sal Khan took math instruction outside of the lecture hall but I will never again be content with handwritten content now that I know about 3blue1brown.
Isn't it great! The video I linked would probably be better understood if you watched the previous episodes in his calculus series, in case you haven't already.

It is just a start though, it doesn't set the standard or qualify as truly understanding the topic. Doing that requires reading and doing the math.

Last edited by Joppy; May 11th, 2017 at 05:55 PM.

 Tags area, curve, intuitive, inverse, slope, understanding

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