Difference between revisions of "009C Sample Final 1, Problem 9"

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(Created page with "<span class="exam">A curve is given in polar coordinates by ::::::<span class="exam"><math>r=\theta</math> ::::::<span class="exam"><math>0\leq \theta \leq 2\pi</math> <span...")
 
 
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[[File:009C_SF1_9_GP.jpg|right|400px]]
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<span class="exam">A curve is given in polar coordinates by  
 
<span class="exam">A curve is given in polar coordinates by  
 
::::::<span class="exam"><math>r=\theta</math>
 
::::::<span class="exam"><math>r=\theta</math>
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!Step 3: &nbsp;
 
!Step 3: &nbsp;
 
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|Since <math style="vertical-align: -1px">\theta=\tan x,</math> we have <math style="vertical-align: -1px">x=\tan^{-1}\theta .</math>
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|Since <math style="vertical-align: -4px">\theta=\tan x,</math> we have <math style="vertical-align: -1px">x=\tan^{-1}\theta .</math>
 
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|So, we have
 
|So, we have

Latest revision as of 17:16, 7 June 2016

009C SF1 9 GP.jpg

A curve is given in polar coordinates by

Find the length of the curve.

Foundations:  
1. The formula for the arc length of a polar curve with is
2. How would you integrate
You could use trig substitution and let
3. Recall that

Solution:

Step 1:  
First, we need to calculate .
Since
Using the formula in Foundations, we have
Step 2:  
Now, we proceed using trig substitution. Let Then,
So, the integral becomes
Step 3:  
Since we have
So, we have
Final Answer:  
  

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