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Ch13Notes

# 6 cylindrical coordinates this idea was introduced at

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Unformatted text preview: pter 11. represents a point in cylindrical coordinates. The first two variables are polar with our third variable being our regular z variable. This coordinate system can represent some surfaces in a compact form. This coordinate system will be very useful when we have a solid that has a circular projection in the xy-plane. But realize the projection does not always have to be in the xy-plane. Once you find which plane has a circular projection then those two variables are re-written in polar while the third variable remains the same. Not only does it make it easier to work with the limits for your triple integral but it can make a triple integral that can’t be solved analytically in the rectangular coordinate system into one that can be solved in the cylindrical system. Here is an example where the polar part is in a different plane: Example: Example: Summary of Section 13.6 1 Sketch the solid represented by a triple integral that is in cylindrical coordinates 2 Sketch the solid represented by a triple integral given in the form: dy r dr d or dx r dr d 3 Set up and evaluate a triple integral with cylindrical coordinates 4 Set up and evaluate a triple integral in the form: dy r dr d or dx r dr d 5 Convert a triple integral from rectangular coordinates to cylindrical coordinates Section 13.7 Spherical Coordinates These coordinates were introduced at the end of chapter...
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