Summing integers using calculus!

Thanks!

#manim #math #proof #visualproof #mathshorts #proofwithoutwords #sums #integers #sumformula

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[wendolinmendoza]

Definitely not the usual nor sensible way of proving this formula, but it is interesting to see yet another proof of it

[owen]

I think this channel could be the best ever for math

[Info_rare]

Very nice.
There is another approach of getting the answer of the integral by applying the area of trapezoid. A=(b+B)/2 = n(n+1)/2 and hence you get the answer 👍

[briancase]

Gauss' method is much simpler and more intuitive. And genius. ☺️

[sarocks]

Hey, can I PLEASE know what application you use to create the masterpiece of videos

[TheEulerID]

My teacher would always insist on putting in the constant for an integral, even if it was a definite one. Use, it will cancel, but that's the way I was taught. For the integral of x + 1/2 with respect to x would be x^2/2 + x/2 + c.

[qwertasdf]

Cant you just extend the graph to x=-1 for a full triangle and use the normal triangle surface formula - 0.25?

[mananagrawal]

You don't really need integral calculus to do any of this. Good co-ordinate geometry is sufficient.