Your teacher seems to be using the same techniques to solve those simple integration problems as the ones that we used in Differential Equations class to solve the intro functions.

Physics equations *usually* use the DiffEq approach, like the "spring" equation involves a hefty equation, and orbital path is easy to write in DiffEq form, but it's its own nightmare to solve.

He's probably just used to using that method for both DiffEq and typical Integrals.


About the Work/Force thing...

I tried to work out why the X disappeared, and... well... I have no idea anymore. I purged tricky details about DiffEq and Calculus after graduating College.

I thought that Work = Force * Distance... so the X should still be there...?

8(

I usually think of d/dX as "you derived an unnamed function with respect to X" and dY/dX as "you derived a function named Y with respect to X"...

d2Y/dX2 "you took the second derivative of Y, with respect to X twice"

makes more sense when you look at:

d2Y/dXdY "you took two derivatives of Y, one with X, one with Y"
(I forgot which one was derived first, but it's not the point.)

Does that help any??

Oh yeah, and don't worry much about when you can call it "the change in" or "with respect to"... all bets are off when you have to integrate them.

[edited by - Nypyren on October 22, 2002 5:03:55 AM]