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March 25, 2017

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Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant between the circles x^2+y^2=64 and x^2 - 8x + y^2 = 0.

  • Calculus - ,

    14 pi

  • Calculus - ,

    the answer u gave me is incorrect. and please tell me the method u tried

  • Calculus - ,

    You don't need Calculus to do this.
    The outer circle has centre at (0,0) and has radius 8
    The other circle has centre (4,0) and radius 4, so the touch at (8,0)
    The big circle has area 64π, so the area in the first quad is 16π
    The smaller circle has area 16π and half of it lies in quad I, so the area in there is 8π

    So the area between the big circle and the little circle in quad I = 16π-8π = 8π

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