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but in the end, it's the same number of calculations as just halving the grain of a normal rectangular sum.

This channel is criminally underrated, I subbed :D

is that not just integrals wth different shapes?

@imagod4796

16 күн бұрын

Yeah, if you take the limit at infinity then its just normal integration

@itsameboyzzzzz7663

15 күн бұрын

Yeah I saw the thumbnail and thought the same thing lmaooo

@greengreen110

15 күн бұрын

yes, if you take the limit as n aproaches infinity then that formula at the end becomes an integral h=(b-a)/n aproaches 0 from the right (a and b are the limits of the integral and b>a) and we notate this as dh then 1/2 * h (y0 + yn) also aproaches 0 and 1/2 * h * 2 * (y1 + y2 +...+ yn-1) aproaches dh * (f(a + h) + f(a + 2h) +...+ f(b - h)) because h tends to 0 then f(a+h) tends to f(a) while f(b-h) tends to f(b) so the entire limit will be dh * (f(a) +...+ f(b)) which is the definition for an integral with limits a and b this kinda requires a little more manipulation of the numbers than when we define integrals by rectangles trapezoids work really well for finitie sums as you can tilt their top to be similar to the function's slope however, when taking the limit to infinity, the slope of the function becomes entirely irrelevant so using rectangles is the simpler option for integration this is why they used trapezoids before calculus and we use rectangles today

Thanks i wrote this in my college, i think the dean wants to give me a fellowship haha

@MasterofBeats

16 күн бұрын

I think he realised i am an alpha