• bh11235@infosec.pub
    13·
    9 months ago
    1. f is a real function from the xy plane to the reals
    2. draw a horizontal-ish band (that is, two lines) creating your favorite wobbly band shape
    3. the integral of f along a single vertical line within the band is itself a function of the line’s x coordinate. Call the function g(x)
    4. What is dg/dx in terms of df/dx? lf the band were perfectly horizontal, it would just be the integral along the vertical line of df/dx within the band. But it’s not, so you add a term to account for the band lines moving
    5. all this assuming f and the band are pretty enough (this is 80% of the theorem statement)
    • lgstarn@kbin.social
      2·
      9 months ago

      For number 4 (or maybe a new number), if a(x) and b(x) are constant, the derivatives d/dx a(x) and d/dx b(x) are zero, so all that is left is that d/dx becomes a partial derivative and can move inside the integral.