Show that impulse is the change of momentum

Explanation

The integral ` int_(ti)^(t f) ` F dt = J is called the impulse and it is equal to change in momentum of the object.
Proof :
if the force is constant over the time interval , then ` int_(ti)^(tf) F dt = F int_(ti)^(t f) dt = F ( t_(f) - t_(i) )= F Delta t = trianglep` is callled the impulsed and it is equal to change in momentum of the object .