how to integrate - When and how do I "set up" an...

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When and how do I “set up” an integral? 1. Determine that an integral needs to be done. If you pay attention to what you are doing you will always recognize the need to integrate due to the fact that some quantity in a formula you are trying to use has a variable value. For instance: t = d v applies to an object moving at constant speed, but what if the speed is not constant over the distance d ? In this case there is no obvious single value of v to use. Similarly F = Gm 1 m 2 d 2 applies to two point objects separated by a distance d , but what if one or both objects have spatial extent? In this case there is no obvious value of d to use. Case 1: The gravitational force due to a uniform ring of radius R and mass M on a particle of mass m located on its axis at a distance x from its center. M m x R Case 2: The time required for an object to travel a distance d from rest if v = a + bx + cx 2 where a and b are constants and x is the distance from the original location. 2.
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how to integrate - When and how do I "set up" an...

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