Calculus 2: The Fundamental Theorem of Calculus (...is not a theorem)

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MathTheBeautiful

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awesome explanations... even when you think you know things... watching your videos - make things clearer and adds something new !!.. thank you so much !!!

salonikothari

Excellent pedagogy. I never thought of dx as the "skin" of the extended area. I'm totally with you as far as travelling in a new (quasi-fantasy) world where things get magnified infinitely or multiplied ad infinitum. Your passion is contagious! Well done.

gribele

I like to think of dx as equal to deltax when deltax is so small that the curve of f(x) approaches a flat line within deltax.

mohammedal-haddad

Nice video, but you failed to make this obvious by what you did at 17:40. You just, for some random reason, decided to divide the surface of x to x+dx with dx. You never explained why you did that, so don't you call it "obvious" at 22:20 when you haven't even explained what you did in the first place.

By your logic it could be called obvious that a rectangle has always the same area as a triangle because if we just, for some random reason, multiply the equation for triangle by 2 then we have the equation for rectangle and because of this it should be obvious that its so. No mister. Nothing is obvious if you don't explain all of the steps and because your mystery step at 17:40 the solution at 22:20 is not "obvious".

A(x + dx) - A(x) is the surface from x to dx, so by dividing it by dx is obviously going to give you the height of the function (which is f(x)), but what has this to do with the question of "how is taking an antiderivative of a function going to calculate the surface area under the function"?

TJ

"who thinks that something else that we haven't considered matters?" 😂

boutiquemaths

Does (1+tanh(x))/(1+tan(x)) have an antiderivative? How to know if there is one?

hericklenin

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