This physics with calculus video tutorial explains how to calculate the impulse of a variable force by calculating the definite integral of the force function with respect to time.

Impulse and Momentum: https://www.youtube.com/watch?v=hODlmGK7pl8

Conservation of Momentum:
https://www.youtube.com/watch?v=Fp7D5D8Bqjc

Rocket Propulsion:
https://www.youtube.com/watch?v=kvAf-Xouj8s

What Really Is a Force?
https://www.youtube.com/watch?v=mril0zFVJXQ

Inelastic Collisions:
https://www.youtube.com/watch?v=C1XuwHLacao

Impulse Momentum Theorem:
https://www.youtube.com/watch?v=1WIECGg71WY

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Force-Time Graphs:
https://www.youtube.com/watch?v=Bv9ry123zck

Ballistic Pendulum Problem:
https://www.youtube.com/watch?v=PUNKqLkELbQ

Elastic Collisions:
https://www.youtube.com/watch?v=CFbo_nBdBco

2D Collision Problems:
https://www.youtube.com/watch?v=9YRgHikdcqs

Impulse & Momentum Test Review:
https://www.youtube.com/watch?v=FfaEbqmvKQA

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Center of Mass Problems:
https://www.youtube.com/watch?v=2uszSnvzBEU

Center of Mass - Calculus:
https://www.youtube.com/watch?v=SWu_i-19Rn0

Intro to Rotational Motion:
https://www.youtube.com/watch?v=WQ9AH2S8B6Y

Full-Length Videos and Worksheets:
https://www.patreon.com/MathScienceTutor/collections

Physics PDF Worksheets:
https://www.video-tutor.net/physics-basic-introduction.html