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Math Help - pplication of double integrals

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    pplication of double integrals

    i need help with this.

    evaluate : Double integral x dA by changing the polr coordinates, where D is the region in the pfirst quadrant that lies between the circles x^2+y^2=4 and x^2+y^2=2x Thank you
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    Quote Originally Posted by fearless901 View Post
    i need help with this.

    evaluate : Double integral x dA by changing the polar coordinates, where D is the region in the first quadrant that lies between the circles x^2+y^2=4 and x^2+y^2=2x Thank you
    The first circle is centred at the origin and has radius 2. Complete the square for the other circle to write it as (x-1)^2+y^2=1. So it has radius 1 and is centred at (1,0). Now draw a diagram. You should be able to see from the diagram that for a given value of θ (between 0 and π/2), the region between the two circles corresponds to r going from 2\cos\theta to 2. Thus \iint_Dx\,dA = \int_0^{\pi/2}\!\!\int_{2\cos\theta}^2r\cos\theta\,rdrd\theta.
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