Answer
The magnitude of the impulse is $~~7.17~kg~m/s$
Work Step by Step
We can find the impulse between $t = 0.500~s$ and $t = 1.25~s$:
$J = \int^{1.25}_{0.500}(12.0-3.00~t^2)~dt$
$J = (12.0~t-t^3)\Big\vert^{1.25}_{0.500}$
$J = [(12.0)(1.25)-(1.25)^3)]- [(12.0)(0.500)-(0.500)^3)]$
$J = 13.047 - 5.875$
$J = 7.17~kg~m/s$
The magnitude of the impulse is $~~7.17~kg~m/s$
