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Double integral problem

  1. May 22, 2008 #1
    Evaluate [tex] \int\ \int_R\ x^2e^ydA[/tex]

    Over the rectangle R with vertices (0,0), (1,0), (1,3) and (0,3).

    My answer:

    [tex] \int\ \int_R\ x^2e^ydA = \int_0^3\ \int_0^1\ x^2e^ydA [/tex]
    [tex] = \int_0^3\ [x^3/3]_0^1 e^y dy[/tex]
    [tex] = 1/3 \int_0^3\ e^ydy [/tex]
    [tex] = 1/3 (e^3-1) [/tex]

    Double integrals are new to me, so if someome could check my answer that would be greatly helpful
  2. jcsd
  3. May 22, 2008 #2


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    looks ok.
  4. May 22, 2008 #3
    seems too easy for 10 marks. There's barely three lines of working there.
  5. May 22, 2008 #4


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    well I dont know if 10marks is much or not. The integral is easy to solve since you had a rectangular area.
  6. May 22, 2008 #5
    The whole 2 hour paper has 100 marks in total. Anyway, thanks for the confirmation.
  7. May 22, 2008 #6
    You are definitely correct. As for the facility with which you did this problem, you're just a superstar at this stuff ;)

    Sometimes profs will toss in easy questions to discern who has, at least, a basic command of the principles involved from those who don't even know what an integrand is.
  8. May 22, 2008 #7
    Have confidence! GJ :)
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