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Double Integral

  1. Oct 4, 2004 #1
    Hi, I've tried to solve this problem over and over and always end up with an enormous second integral that seems to never reduce to simpler terms.

    [tex]\int\int(x^2+xy+1)dydx[/tex]

    Where the bounds of the inner integral are [tex][x-1,xcos(2(\pi)x)][/tex] and the outer integral are [tex][1,0][/tex]

    Thank you for any help in advance. Any would be great.
     
  2. jcsd
  3. Oct 4, 2004 #2

    Tide

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    I get

    [tex]-\frac {116 \pi^2 + 153}{192 \pi^2}[/tex]

    The inner integral came out to be

    [tex]x(x^2+1) \cos {2\pi x} - \frac {x^3 \sin^2 2\pi x}{2} -x^3 + 2x^2-\frac {3x}{2} + 1[/tex]
     
  4. Oct 4, 2004 #3
    Thank you Tide.

    For the inner integral I get:

    [tex]x^3\cos^2(2(\pi)x)+(x(\cos^2(2(\pi)x)))/2+x\cos^2(2(\pi)x)-x(x-1)-((x(x-1)^2)/2)-x+1[/tex]

    I can simplify the second half but not the first. Is there some trick like a substitution to going further from this point, because I've tried integrating this and it was a monster... 2 pages and I couldnt reach a solution.
     
  5. Oct 4, 2004 #4
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