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Math Help - polar enclossed area integral mmn 15 2b

  1. #1
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    polar enclossed area integral mmn 15 2b

    i forgot to mention that y>=0 and theta is from 0 to pi
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  2. #2
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    Drawing them would be easiest if you converted both equations to cartesians, using \displaystyle x = r\cos{\theta}, y = r\sin{\theta}, x^2 + y^2 = r^2.
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    was told to use polar by my prof
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    But you give one equation, x^2+ y^2= 1, in Cartesian coordinates! In polar coordinates, that is r= 1. That should be easy to draw. As for r= 1+ cos(\theta), that is what is called a "cardioid". Look it up. As far as graphing is concerned, you could just use the "old fashioned" way- calculate r for a number of \theta values. The are beween them will be the integral of f_1(\theta)- f_2(\theta)= (1+ cos(\theta))- 1= cos(\theta). And the integration will be between values of \theta where the graphs cross: solve 1+ cos(\theta)= 1.
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  5. #5
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    Quote Originally Posted by transgalactic View Post
    was told to use polar by my prof
    Yes, use polars to evaluate the integral, but you can use Cartesians to aid in graphing...
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  6. #6
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    i managed to draw it
    but when i made 1=1+sin theta
    theta=pi*k
    but the drawing gives me pi/2 point
    i dont know how to complerte the integral
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