Sorry to cut in the thread like that but i beleive i can add something that might help ya.
I have studied what your talking about McNeo and I must say at first it seams hard and then it gets easyier
The wavy thing is an integration sign and the number under it is the start of the section you wish to do the integration on and the top one is the end.
Basicaly an integration is the surface under a curve if you were wondering and a derivation if a "tangente" slope.(french is my native language so please someone translate the quoted word...)
Im not sure all your examples are solved correctly since i barely checked em but they look ok.
Mcneo, you are correct with your derivative but but watch where you put those dy/dx things in your integration also pull the constants out of the thing you are intergrating cuz you made a some mistakes due to those. Don't worry, everyone sucks at intergration on their first try. I know I messed it up big time and most people in college still have trouble with it. there a several other rules that can be used. You used the "chain rule" but there is also the quotient rule and the product rule.
dy/dx means (in this context, there are others) take the derivative of a function with output y with respect to x. so take the derivative of all the stuff on the x side of the function.
Oh Gato, you know Single Variable Calc?
Cuz if you do, that would be cool. I may be able to ask you about some calc 2 problems.
I guess I should have asked before this.