/sci/ - Science & Math

>>8964524

>>8964524
if you graph if it's really intuitive. try graphing something retardedly simple such as y=x and it's derivative y=1

>>8964524
>But how it mathematically works?
Mathematically it works by approximating the area under a curve with thin rectangles. The thinner the rectangles, the better approximation you get. When the rectangles are infinitesimally thin with height [math]f(a)[/math] at [math]a[/math], the area of that rectangle is [math]f(x)\cdot ds[/math] where [math]ds[/math] is the infinitesimally thin width. The integral is the sum over all ares of such infinitesimally thin rectangles, that is, the area under the curve.

>how could giving the primitive of an equation can give us the volume?
Read up on the Fundamental Theorem of Calculus, which explains why the primitive function of some function can be used to find the area under a function.

>>8964531
That's the redpill on Integrals.

both

>>8964531
All that only to integrate a few more weird integrals lmao.

>>8965056
That is a lot more than few considering it is for a general measure space (not just R^n with the lebesgue measure).

[math]\int_a^b f(x)dx=\int_a^b \int_0^{f(x)}dydx=\int_\Omega dA[\math]

[math]\int_a^b f(x)dx=\int_a^b \int_0^{f(x)}dydx=\int_\Omega dA[/math]

>>8964579
>infinitesimally
*cue the autistic screeching about "muh limits"