What's the error in my derivations? (impulse/momentum)

[Kyuutoryuu]

(Change in momentum is the area under a force against time curve.)

(Force is the time derivative of momentum.)

Using separation of varibles, you get Fdt=dp. Integrate both sides, you get that the integral of Force with respect to time is equal to p. This seems to imply that p, momentum, is equal to change in momentum?

 

[Svein]

Using separation of varibles, you get Fdt=dp. Integrate both sides, you get that the integral of Force with respect to time is equal to p. This seems to imply that p, momentum, is equal to change in momentum?

Look at your first equation. It defines the integral of F (in your sense) as a change in momentum.

 

[Orodruin]

(Change in momentum is the area under a force against time curve.)

(Force is the time derivative of momentum.)

Using separation of varibles, you get Fdt=dp. Integrate both sides, you get that the integral of Force with respect to time is equal to p. This seems to imply that p, momentum, is equal to change in momentum?

You forgot the integration constant. Momentum after = momentum before + change in momentum.