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Difficult Double Integrals

  1. Apr 19, 2012 #1
    Evaluate ∫∫xexp(xy)dA,
    and R (over which the integrand is to be integrated) is {(x,y)|0≤x,y≤1}.
    Could someone explain how this is to be done.
     
  2. jcsd
  3. Apr 19, 2012 #2

    tiny-tim

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    hi hivesaeed4! :wink:

    dA = dxdy

    try integrating wrt y first :smile:
     
  4. Apr 19, 2012 #3
    My Bad. What I meant was what are the limits we should take for x and y. We are given one limit (either upper or lower limit) in each case. How do we find the second one for both x and y?
     
  5. Apr 19, 2012 #4

    tiny-tim

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    oh i see!! :biggrin:

    no, {(x,y)|0≤x,y≤1} is two limits …

    the limits apply to both x and y (separately) :wink:
     
  6. Apr 19, 2012 #5
    Look, let me tell you how I see the limits and correct me if I'm wrong.

    The lower limit of x is 0. We have to find its upper limit.

    The upper limit of y is 1. We have to find its lower limit.

    The reason we have to find the upper limit of x and lower limit of y is that they are required for the integration.

    Correct?

    Also, please tell me how to find the upper limit of x and lower limit of y.
     
  7. Apr 19, 2012 #6

    tiny-tim

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    no, {(x,y)|0≤x,y≤1} is a shorthand way of saying {(x,y)|0≤x≤1} and {(x,y)|0≤y≤1} :wink:
     
  8. Apr 19, 2012 #7
    Thanks tiny-tim. Thanks alot. That question had me very confused.
     
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