>tfw finally thought I understood what derivative and integral functions are on an intuitive level but it turned out I was just confused again
ENOUGH
Tfw finally thought I understood what derivative and integral functions are on an intuitive level but it turned out I...
Elijah Stewart
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Carson Lewis
Once you "get it" then dynamic systems will never look the same, "seeing" calculus is the sci-pill.
Christopher Reed
>"seeing"
It's just like those fucking magic eye pictures, isn't it? I could never get those to work REEEEEEE
Brody Phillips
>derivative functions
A derivative function of f is a function that maps the independent variable to the slopes of the tangent lines on f. An integral function of f is a function that maps the independent variable to the enclosed areas between f and the x axis. What is so confusing about this?
Cooper Rodriguez
>on an intuitive level
You probably don't know what intuiting is like because you're autistic.
James Robinson
Not OP but I was confused as to why the integral is the area of the graph. I think I see what he means by "intuity" because with simpler operations like adding, the "opposite" would be subtracting. It just seems weird the opposite of a derivative (slope) is the area under the graph.
Luke Sanders
>PROBABLYANALGEBRAMISTAKE
Sebastian Cook
You can consider an integral to be the limit of sum of areas. So when you integral a function, you're taking the sum of a bunch of areal values of that function, hence, it gives you the area under that curve, right? But then, if you differentiate the integral, you're taking the instantaneous rate of change of the area, which is the original function, hence, the two cancel each other out.
You could also consider the (technically incorrect but still intuitive) argument, that given a function f, and its derivative df/dx, then you integrate it with respect to x, you get integral(df/dx *dx), so you "cancel" the "dx"s (this totally isn't true, mind you, I'm just trying to give you an understanding), you're left with the integral of df, which are tiny bits of the original function f, so if you integrate all those tiny bits of f, you get f.
Lucas James
Autists are the only ones who intuit. NTs can only muster a pale imitation.
Jace Garcia
If you look up Euler's method, it is pretty clear that making an integral function of a derivative function of f just produces the function f (up to a constant, at least). Additionally, if you look up the fundamental theorem of calculus, it is clear that making a derivative function of an integral function of f just produces f again (as the area of the integral function bounded by f, the x axis, the line x = x_0 and the line x = x_0 + h, where h is a very small positive number, is approximentally f(x_0)*(x_0 + h - x_0) = f(x_0)*h. During differentiation, you take this number, and divide it by (x_0 + h - x_0) = h, so the derivative function of the integral function of f at the point x_0 would just be f(x_0)).