Difference between revisions of "009C Sample Final 1, Problem 9"
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!Step 3:  !Step 3:  
    
−  Since <math style="verticalalign:   +  Since <math style="verticalalign: 4px">\theta=\tan x,</math> we have <math style="verticalalign: 1px">x=\tan^{1}\theta .</math> 
    
So, we have  So, we have 
Latest revision as of 17:16, 7 June 2016
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 

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: 
