Why does dP/dt = 0 imply constant total momentum?

[gibberingmouther]

Homework Statement

the rate of change of the total momentum in a system with respect to time is zero.
thus, my textbook says, the total momentum of that system is constant.

i'd like to understand how one implies the other if anyone could give me a conceptual explanation? i understand the steps to get the derivative of total momentum equation. i just don't have a good grasp on how that implies that the total momentum of the system is constant.

Homework Equations

dP/dt = 0 (where P is a vector quantity and is the total momentum of a system)

The Attempt at a Solution

integrate dP/dt = 0 and you get P = C, a constant. that is one way to get the answer but i am not satisfied. i want a better explanation.

 

[Orodruin]

integrate dP/dt = 0 and you get P = C, a constant. that is one way to get the answer but i am not satisfied. i want a better explanation.

There is no "better" explanation than the explanation. The primitive function of zero is a constant. There is absolutely nothing more to it. The derivative with respect to time equal to zero literally tells you that the function does not change with time.