a quick proof of the Fundamental Theorem of Calculus

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[SaidVSMath]

I’ve literally been looking for a satisfying intuitive proof of the FTC for like 5 years THANK YOU

[Neuranet]

I appreciate the work you’re doing here

[boredomisbliss]

There's some details missing from the "can be chosen" part of the proof. In order to do this you have to know the limit exists, and that it doesn't depend on how you choose x* (or even the xks).

[christopherdavies]

bruh i knew i shoulda started that khan academy course

[markusklyver]

This assumes that f is continuous for the MVT to apply. Of course this is given since f' exists.

[soumyaj]

Doesn't the mean value theorem itself require the fundamental theorem of calculus to work?

[abdullahaddous]

This “collapsing” property is the same thing I was told to understand Greene’s theorem! (Which is guess is a generalization of the fundamental theorem of calculus.) Is there a connection or is this a coincidence?

[williamwarren]

Are we assuming that we can do a uniform mesh for the integral? I havent done Riemann sums in a while

[dougr.]

The RHS of the board is obscured by YouTube buttons

[guntherbeer]

This is just an appeal to another theorem. It lacks intuition. If you drop the rigor and think in terms of position and velocity, the statement is intuitively obvious and the magic disappears.

[NewCalculus]

You like copying my ideas without giving me credit, eh.

[omarsanchez]

Great....now go implement it to make us some tacos

[anshumanagrawal]

This doesn't follow from the mean value theorem. In fact it isn't even true in general