Have you heard of using wedges in calculus to approach integration differently?

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jerromyjon
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I can't seem to find anything about what I am thinking about but it has to do with a possibly unique idea I am just wondering if any has ever heard of any such "variation" of calculus. I'm certainly not fluent with even basic calculus, but I can model the "area under a curve" and the aspect that doesn't fit is the x/y grid. What I am considering is way to complex for me to grasp its implications, but the basic idea is to flip the problem around to a set of identical wedges which puts the chord of the curve as the "width" of the wedges. I haven't gotten any further than that and it is a very shaky hypothetical idea I'm just looking to see if anyone knows anything that sounds similar?
 
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jerromyjon said:
I can model the "area under a curve" and the aspect that doesn't fit is the x/y grid.
Are you saying that you don't understand how you can calculate the area under a curve using rectangles?

If that's what you meant, I would advise getting an understanding of that technique before attempting to find the area using wedge shapes. A rectangle has a very simple area: width x length. Do you know a corresponding formula for the area of a wedge?

Another form of integration (polar integrals) uses a different shape entirely.
 
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Mark44 said:
Are you saying that you don't understand how you can calculate the area under a curve using rectangles?
I've been sitting here counting pixels trying to find any patterns in progressively larger curves or figure out what to try next.
Mark44 said:
Another form of integration (polar integrals) uses a different shape entirely.
Ah, polar integrals sounds promising, I'll have to check that out when I have time. Thanks a lot!
 
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Mark44 said:
Are you saying that you don't understand how you can calculate the area under a curve using rectangles?
jerromyjon said:
I've been sitting here counting pixels trying to find any patterns in progressively larger curves or figure out what to try next.
You quoted what I asked, but didn't answer my question. What does counting pixels have to do with integration?
 
Mark44 said:
What does counting pixels have to do with integration?
Different methods to get the same results. I've also been doing some origami of sorts...
 
Mark44 said:
Another form of integration (polar integrals) uses a different shape entirely.
This is exactly what I was trying to figure out in a bass ackwards kind of way. :mad: Thanks again! :cool:
 
Mark44 said:
What does counting pixels have to do with integration?
I don't do the math, I make my computer do it exactly how I think it, to accomplish the results I intend. I try, not to think, harder than I have to. :smile:
 
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