Parametrization

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Parametrization is a technique in calculus for expressing multiple variables in terms of only one variable, which is usually depicted as "t", over a specified range.

The most common parametrization is for a circle centered at the origin in the xy-plane:

  • x = rcos(t)
  • y = rsin(t)
  • z = 0
  • 0 \le t \le \pi

Always remember to be precise in determining the new limits on the new parameter t.

This technique is particularly useful for calculating extrema and line integrals.

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