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Iterated Integrals

  1. Jun 27, 2010 #1
    1. The problem statement, all variables and given/known data

    Evaluate the iterated integral [URL]https://webwork.csun.edu/webwork2_files/tmp/equations/e4/1efafbd0e820388c5c73acc695601b1.png[/URL]

    2. Relevant equations

    Fundamental Theorem of Calculus & Fubini's Theorem

    3. The attempt at a solution

    I have been working on this problem for the last hour and haven't been able to solve it thus far. I integrated the inside of the integral with respect to y from 4 to 3, and then integrated the result from the first integral with respect to x from 2 to 1. In the process, I used substitution to solve the integrals.

    The answer I keep on getting is ([tex]1/(4(3x+4)^4)[/tex]) - ([tex]1/(4(3x+3)^4)[/tex]) and solve from x= 2 to 1 which results in a small fractional answer of 7.5674005*10^(-5). But my online program keeps on saying its incorrect.

    Can anyone give me a heads up as to where I am going wrong? This is one of the few iterated integrals that is giving me problems right now :(
     
    Last edited by a moderator: Apr 25, 2017
  2. jcsd
  3. Jun 27, 2010 #2
    Its better to post your work.
    Here is a start:
    the integration of 1/(3x+y)^2 with respect to y from y=3 to y=4 is :
    (-1/3x+4) - (1/3x+3)
    and this result is easy to integrate with repsect to x, isn't it ?
     
  4. Jun 27, 2010 #3
    I found out what my problem was. I made the stupid mistake of differentiating u^-2 when I should have integrated. Thank you. Your first integration was correct, and that was what was causing my mistake.
     
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