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Section 3-3 : Area with Parametric Equations

For problems 1 – 3 determine the area of the region below the parametric curve given by the set of parametric equations. For each problem you may assume that each curve traces out exactly once from right to left for the given range of t. For these problems you should only use the given parametric equations to determine the answer.

  1. \(x = {t^2} + 5t - 1\hspace{0.25in} y = 40 - {t^2}\hspace{0.25in} - 2 \le t \le 5\)
  2. \(\displaystyle x = 3{\cos ^2}\left( t \right) - {\sin ^2}\left( t \right)\hspace{0.25in} y = 6 + \cos \left( t \right)\hspace{0.25in} - \frac{\pi }{2} \le t \le 0\)
  3. \(x = {{\bf{e}}^{\frac{1}{4}t}} - 2\hspace{0.25in} y = 4 + {{\bf{e}}^{\frac{1}{4}t}} - {{\bf{e}}^{\frac{1}{2}t}}\hspace{0.25in} - 6 \le t \le 1\)