Line Integrals

Line Integrals - Lizzie Wagner Line Integrals Line...

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Lizzie Wagner Line Integrals Line integrals can be calculated by two methods: with respect to arclength and with respect to coordinate variables. When integrating through arclength, we know a property along the line, while when we integrate with coordinate variables, we know the vector field around the line. Although this may sound like a subtle difference now, but their applications are different and how they are calculated also contrast. The uses for calculating through arclength include mass of a thin object, like a wire, and require knowing a specific characteristic at every point on the line, for example density. When calculating mass, it is not essential to know which direction the particle is moving along the curve. A real life example of this is when someone needs a certain length of string, but must make sure it is not too heavy to use in their design. Arclength is acceptable to use in this sort of computation because there is no such thing as negative mass or negative density. However, this is the place where the two forms of line
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This note was uploaded on 04/18/2008 for the course MATH 234 taught by Professor Boeri during the Winter '08 term at Northwestern.

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Line Integrals - Lizzie Wagner Line Integrals Line...

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