March 17th, 2011, 01:56 PM  #1 
Newbie Joined: Mar 2011 Posts: 20 Thanks: 0  Finding area using integration
Find the area formed by intersection of parabola and circle ?

March 17th, 2011, 03:44 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Finding area using integration
We can simplify this problem a bit by rotating the parabola radians to get and using the even function rule, we have: Can you go from here? 
March 17th, 2011, 03:54 PM  #3 
Newbie Joined: Mar 2011 Posts: 20 Thanks: 0  Re: Finding area using integration
Yes I can...it's ok ... Thanks!

March 17th, 2011, 04:24 PM  #4 
Newbie Joined: Mar 2011 Posts: 20 Thanks: 0  Re: Finding area using integration
I'm having a new problem: The curve divides the area bounded by the curve into two parts. Find that areas! 
March 17th, 2011, 10:12 PM  #5 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Finding area using integration
Here is a graph of the two curves (with a = 1): [attachment=0:2lkiuwf7]polar02.gif[/attachment:2lkiuwf7] I would convert the equations to polar form: Next, let's rotate the rose ?/4 radians: Now we need the angle in the first quadrant where the two curves intersect: Thus, we may find the area inside the polar rose within the circle as: The total area enclosed by the polar rose is: Thus, the area outside the circle, but within the polar rose is: 
March 18th, 2011, 03:06 AM  #6  
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0  Quote:
 

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