- #1

hideelo

- 91

- 15

If I have an equation of the following form

d(f(x,y)) = h(x,y)dx

the approach they then take is to "integrate both sides" and they remain with the following equation

f(x,y) = g(x,y) + c where g(x,y) = ∫h(x,y)dx

the integration on the right is clearly with respect to x, I am not so clear as to what they are doing on the left however. It seems like they are asserting that the integral of the derivative of a function is the function itself. But with respect to what are they integrating it? Is this only with respect to x? If so then the answer is wrong since ∫ d(f(x,y))dx is in general not f(x,y) . Is this some sort of line integral and we are using gradient theorem? If so are we doing the same thing on the other side of the equation? I don't think so, as we are only integrating with respect to x

The other confusion comes from the following, if have the same initial equation as above, d(f(x,y)) = h(x,y)dx is that the same as (d/dx)(f(x,y)) = h(x,y)? If yes, how so? How about if I have something of the following form ∂/∂x (f(x,y)) = h(x,y)?

TIA