# What is the integral of the momentum function?

If we assume that mass is constant, then we can factor it out:

Then, by using the power rule with respect to integrals:

Note that this is equivalent to the formula for kinetic energy.

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The integral of the momentum function, denoted as ∫p(t) dt, represents the change in momentum over a specified time interval. It is calculated by integrating the momentum function with respect to time over that interval. Mathematically, if the momentum function is given as p(t), where t represents time, then the integral of p(t) dt from time t₁ to t₂ (denoted as ∫p(t) dt from t₁ to t₂) can be found by evaluating the antiderivative of p(t) with respect to t over the interval [t₁, t₂]. The result represents the total change in momentum during that time interval.

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