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Assignment Problems Notice
Please do not email me to get solutions and/or answers to these problems. I will not give them out under any circumstances nor will I respond to any requests to do so. The intent of these problems is for instructors to use them for assignments and having solutions/answers easily available defeats that purpose.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
Section 9.3 : 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.
- \(x = {t^2} + 5t - 1\hspace{0.25in} y = 40 - {t^2}\hspace{0.25in} - 2 \le t \le 5\)
- \(\displaystyle x = 3{\cos ^2}\left( t \right) - {\sin ^2}\left( t \right)\hspace{0.25in} y = 6 + \cos \left( t \right)\hspace{0.25in} - \frac{\pi }{2} \le t \le 0\)
- \(x = {{\bf{e}}^{\frac{1}{4}t}} - 2\hspace{0.25in} y = 4 + {{\bf{e}}^{\frac{1}{4}t}} - {{\bf{e}}^{\frac{1}{2}t}}\hspace{0.25in} - 6 \le t \le 1\)