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Math Help - polar coordinated two variable calculus

  1. #1
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    polar coordinated two variable calculus

    Using polar coordinates evaluate

    int int over D 3(x+y) and D is x^2 + y^2 <=9, x>=0

    Ok, I have

    int (between -pi/2 and pi/2) d theta . int(between 3 and 0) 3r^2(costheta + sintheta)

    giving 18

    is this right?

    it seems i'm missing something I think

    many thanks
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  2. #2
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    Quote Originally Posted by James0502 View Post
    Using polar coordinates evaluate

    int int over D 3(x+y) and D is x^2 + y^2 <=9, x>=0

    Ok, I have

    int (between -pi/2 and pi/2) d theta . int(between 3 and 0) 3r^2(costheta + sintheta)

    giving 18

    is this right?

    it seems i'm missing something I think

    many thanks
    Although the integral, 3\int_{\theta= -\pi/2}^{\pi/2} \int_{r= 0}^3 r^2(cos(\theta)+ sin(\theta) dr d\theta is correct, I do NOT get 18 for that integral. Could you show how you got that?
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  3. #3
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    erm.. ok

    integrate first wrt r - to give 9 (cos theta + sin theta) then wrt theta to give
    9(sin theta - cos theta)

    putting limits in gives 18

    oh wait

    i need to multiply by 3?
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