Difference between revisions of "009C Sample Final 3, Problem 8"

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<span class="exam">A curve is given in polar coordinates by &nbsp;<math style="vertical-align: -2px">r=4+3\sin \theta</math>
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<span class="exam">A curve is given in polar coordinates by &nbsp;<math style="vertical-align: -2px">r=4+3\sin \theta.</math>
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::<math>0\leq \theta \leq 2\pi</math>
 
  
 
<span class="exam">(a) Sketch the curve.
 
<span class="exam">(a) Sketch the curve.
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<span class="exam">(b) Find the area enclosed by the curve.
 
<span class="exam">(b) Find the area enclosed by the curve.
  
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!Foundations: &nbsp;
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[[009C Sample Final 3, Problem 8 Solution|'''<u>Solution</u>''']]
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|The area under a polar curve &nbsp; <math style="vertical-align: -5px">r=f(\theta)</math>&nbsp; is given by
 
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&nbsp; &nbsp; &nbsp; &nbsp;<math>\int_{\alpha_1}^{\alpha_2} \frac{1}{2}r^2~d\theta</math>&nbsp; for appropriate values of &nbsp;<math>\alpha_1,\alpha_2.</math>
 
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'''Solution:'''
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[[009C Sample Final 3, Problem 8 Detailed Solution|'''<u>Detailed Solution</u>''']]
  
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!(a) &nbsp;
 
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'''(b)'''
 
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!Step 1: &nbsp;
 
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!Step 2: &nbsp;
 
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!Final Answer: &nbsp;
 
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|&nbsp;&nbsp; '''(a)'''
 
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|&nbsp;&nbsp; '''(b)'''
 
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[[009C_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]
 
[[009C_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]

Latest revision as of 16:30, 3 December 2017

A curve is given in polar coordinates by  

(a) Sketch the curve.

(b) Find the area enclosed by the curve.

Solution


Detailed Solution


Return to Sample Exam

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