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Section 3-9 : Arc Length with Polar Coordinates

  1. 1. Determine the length of the following polar curve. You may assume that the curve traces out exactly once for the given range of \(\theta \). \[r = - 4\sin \theta , \,\, 0 \le \theta \le \pi \] Solution

For problems 2 and 3 set up, but do not evaluate, an integral that gives the length of the given polar curve. For these problems you may assume that the curve traces out exactly once for the given range of \(\theta \).

  1. \(r = \theta \cos \theta \), \(0 \le \theta \le \pi \) Solution
  2. \(r = \cos \left( {2\theta } \right) + \sin \left( {3\theta } \right)\), \(0 \le \theta \le 2\pi \) Solution