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

[jerromyjon]

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?

 

[Mark44]

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.

 

[jerromyjon]

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.

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!

 

[Mark44]

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.

You quoted what I asked, but didn't answer my question. What does counting pixels have to do with integration?

 

[jerromyjon]

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...

 

[jerromyjon]

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. Thanks again!

 

[jerromyjon]

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.