October 25th, 2014, 09:15 AM  #1 
Newbie Joined: Sep 2014 From: USA Posts: 8 Thanks: 0  Finding the area inside a cardiod
I messed up towards the end but can't find my error. $\displaystyle 2[1/2âˆ« (Ï€/2) to (Ï€/2) , (1 2sin(Î¸) + sin^2(Î¸))$d(Î¸) I made two integrals $\displaystyle 2[1/2âˆ«(Ï€/2) to (Ï€/2), (1sin(Î¸))] dÎ¸+ 2[1/2âˆ«(Ï€/2) to (Ï€/2), (sin^2(Î¸))] dÎ¸ $ Then I derived it. 2[1/2 (((Î¸)+2cos(Î¸) + 1cos(2Î¸)))] Ï€/2 to  Ï€/2 When evaluate each side I keep getting the wrong answer. I keep getting 0 or Ï€, I have been working on it for 3 days already. Last edited by j423; October 25th, 2014 at 09:17 AM. 
October 25th, 2014, 09:45 AM  #2  
Math Team Joined: Jul 2011 From: Texas Posts: 2,924 Thanks: 1521  Quote:
For your last term in your original integrand ... $\displaystyle \sin^2{\theta} = \frac{1\cos(2\theta)}{2}$ antiderivative is $\displaystyle \frac{1}{2}\left(\theta  \frac{\sin(2\theta)}{2}\right)$  
October 25th, 2014, 10:11 AM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,657 Thanks: 2635 Math Focus: Mainly analysis and algebra 
I can't see where the 2 in the $2\cos \theta$ term came from either.

October 25th, 2014, 01:08 PM  #4 
Newbie Joined: Sep 2014 From: USA Posts: 8 Thanks: 0 
Yeah, I see that now. I did something weird on my paper too! thanks


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area, cardiod, finding, inside 
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