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Math Help - Integrate

  1. #1
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    Integrate

    Im having trouble with my limits, and whether or not im on the right direction

    My question is:
    Let R be the region in the first quadrant bounded by the line y=x and the curve
    x^4 + (xy)^2 = y^2.

    My double integral is
    (1+ x^2 + y^2)^-2 dA

    heres what im doing so far..
    and then evaluate..Am i right, limits correct and everything


    IN THE FUNCTION, SHOULD BE R/(1 + R^2)^2
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  2. #2
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    \displaystyle x^4 + (xy)^2 = y^2\rightarrow r^2=tan^2(\theta)

    \displaystyle y=x\rightarrow tan(\theta)=1

    \displaystyle \int\int \frac{r}{(1+r^2)^2}drd\theta

    Now setup your bounds
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  3. #3
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    thanks for the help so far,

    so what your saying is
    theta goes from 0-pie/4
    and r goes from (? -tan)
    whats the lower limit for r?
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  4. #4
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    Have you drawn the graph?
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  5. #5
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    are the limits 0-tan for r
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  6. #6
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    yes
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  7. #7
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    thnx a bunch partner
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