Iterated Integral

  1. 1. The problem statement, all variables and given/known data
    Evaluate the iterated integral I = [tex] \int^{1}_{0}\int^{1+y}_{1-y} (6y^2+ 10x) dxdy [/tex]


    2. Relevant equations

    . . . ?

    3. The attempt at a solution
    Integrate with respect to x gives me the following equation.
    [tex] \int^{1}_{0} 6xy^2 + 5x^2 dy [/tex]
    I plug in y+1 and y-1 into x and get the following
    6y2+12y3+6y4+5+10y+5y2-6y+12y3-6y4-5+10y-5y2
    Most of the stuff cancels out giving me
    12y3+12y3+10y+10y
    which simplifies to
    [tex] \int^{1}_{0} 24y^3+20y dy [/tex]
    and after integration I get
    6y4+10y2
    and after plugging in my numbers I get
    6+10 = 16 which is wrong. I am not sure where I screwed up.
     
  2. jcsd
  3. jhae2.718

    jhae2.718 1,160
    Gold Member

    Don't use sup in LaTeX; exponents are indicated by ^, with braces {} if the exponent is more than one character long.

    I only briefly looked at your work, but you might want to check your substitution of limits in the first integrand.
     
  4. jhae2.718

    jhae2.718 1,160
    Gold Member

    <double post>
     
  5. You, were right! I screwed up by substituting the limits into the y instead of x by mistake. Thanks a lot.
     
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