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## Main Question or Discussion Point

In my Halliday Resnick Walker book, they derive the equations of kinematics using integrals in a small section after the algebraic derivation. I'm extremely confused by the calculus, however. Sorry if my questions are unclear.

They say that [tex]\frac{dx}{dt}=v⇒dx=v\cdot dt[/tex]. This first step itself confuses me. Are [itex]dx[/itex] and [itex]dy[/itex] supposed to be infinitesmally small values? If so, are they constants? I thought that this is just a notation that shows the derivative of position with respect to time, but is this for a specific time [itex]t[/itex] or does it represent some property that holds for all times?

Second, they integrate each side of [itex]dx=v\cdot dt[/itex], and end up with [itex]\int dx=\int v \: dt[/itex], with [itex]dt[/itex] as the integral term of the RHS. That made no sense to me; how does [itex]dt[/itex] go from being a constant to an integral term simply representing what variable you're integrating with respect to?

Again, sorry if my question is unclear.

Thanks in advance!

They say that [tex]\frac{dx}{dt}=v⇒dx=v\cdot dt[/tex]. This first step itself confuses me. Are [itex]dx[/itex] and [itex]dy[/itex] supposed to be infinitesmally small values? If so, are they constants? I thought that this is just a notation that shows the derivative of position with respect to time, but is this for a specific time [itex]t[/itex] or does it represent some property that holds for all times?

Second, they integrate each side of [itex]dx=v\cdot dt[/itex], and end up with [itex]\int dx=\int v \: dt[/itex], with [itex]dt[/itex] as the integral term of the RHS. That made no sense to me; how does [itex]dt[/itex] go from being a constant to an integral term simply representing what variable you're integrating with respect to?

Again, sorry if my question is unclear.

Thanks in advance!

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