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March 17th, 2011, 01:56 PM   #1
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Finding area using integration

Find the area formed by intersection of parabola and circle ?
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March 17th, 2011, 03:44 PM   #2
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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?
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March 17th, 2011, 03:54 PM   #3
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Re: Finding area using integration

Yes I can...it's ok ... Thanks!
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March 17th, 2011, 04:24 PM   #4
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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!
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March 17th, 2011, 10:12 PM   #5
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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:

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March 18th, 2011, 03:06 AM   #6
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Quote:
Originally Posted by tulipe
Find the area formed by intersection of parabola and circle ?
Find the area formed by intersection of parabola and circle Both statements are equivalent because circle's centre is (0, 0), therefore area formed by parabola's intersection and circle will have no difference.

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