Basic calculus question (kinematics)

[tolove]

Could someone point me to the proof or reasoning behind the steps:

1) a = dv/dt
2) a dt = dv
3) ∫a dt = ∫dv

I know this works, but I'm missing understanding in the math behind it, and I'm not sure what to type into google.

Thank you very much

 

[arildno]

1) is the definition of acceleration, i.e, the derivative of velocity with respect to time.
2)+3) are silly pseudo-steps, the mathematically CORRECT next step from 1) is:
2a) $$\int{a}dt=\int\frac{dv}{dt}dt$$
3a) Now, using integration by substitution on the right-hand integral, we may, if we like, rewrite 2a) as:
$$\int{a}dt=\int{dv}$$