late night revelation whilst doing physics about maths

ok. this is deep, from a 2 unit perspective, especially one taught by the teacher we have (no name-dropping)

so you know how the symbol for differentiation, which finds the gradient, is dy/dx?

its the change in y / the change in x

this is equal to the gradient formula, y2-y1 / x2-x1

also if you take like, for example y = 4x

using differentiation we can immediately find

y' = 4

do it manually:

at x=1, y=4

at x=2, y=8

m = 8 - 4 / 2 - 1

= 4/1

=4

and then in integration because its the reverse of differentiation, you times it by dx instead of dividing it by. thats what the dx on the end is

yeah, its 1 am.