the area bounded by the line and the axes of a velocity-time graph is equal to the displacement of an object during that particular time period
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Friction is the force you get when you (for example) Rub something with another, it's a force that may generate heat and even some resistance. Another example is rubbing your hands together, they get hot, therefore friction is working, without friction you wouldn't be able to stop moving.
Differentiation in its simplest of terms means breaking something into small parts. On the other hand, integration is taking those really small parts and gluing them in the right order. In short, these terms are the direct opposite or inverses of each other. The term which can tell you how fast you are going at a moment in time at ones current location is called a derivative. The term on the other hand, which can tell you how far you have travelled if you have been keeping track of your location and your time is what an integral is referred to. It is like differentiation only needs knowledge on the local neighbourhood while integration will need the knowledge on a global knowledge.
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