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May 6th, 2017, 04:13 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, 04:48 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,508 Thanks: 1234  
May 11th, 2017, 04:45 PM  #4  
Newbie Joined: Apr 2017 From: USA Posts: 11 Thanks: 0 
Thanks for the great responses. Quote: Quote:
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, 04:49 PM  #5  
Senior Member Joined: Feb 2016 From: Australia Posts: 1,089 Thanks: 366 Math Focus: Yet to find out.  Quote:
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 04:55 PM.  

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