Double Integral

Discussion in 'Math' started by susi, May 12, 2005.

  1. susi

    Thread Starter Active Member

    Jun 4, 2004
    31
    0
    Hello , I am facing lil problem in solving this:
    If anyone help , it would be great..Well the problem is abt
    evaluating double integral.

    Q: Evaluate:

    ∫ ∫ [xy/ √ (x^2+y^2+1)]dA


    over the rectangle R=(x,y):0 ≤ x ≤ 2,0 ≤ y ≤ 2
    also draw the double integral is independent of order of integration.
     
  2. haditya

    Senior Member

    Jan 19, 2004
    220
    0
    lets integrate 1st wrt to x

    2 2
    ∫ ∫ xy dx dy/ √ (x^2+y^2+1)
    0 0

    put x^2+y^2+1=t

    2 y^2+1
    0.5 ∫ ∫ dt ydy/ √ t
    0 y^2+5


    then its quite easy to solve
    the terms are seperable

    i d hav typed it buts kinda difficult to type these integrals
     
  3. haditya

    Senior Member

    Jan 19, 2004
    220
    0
    its independent of the order of integration because the limits are constants in the 1st integral
     
  4. susi

    Thread Starter Active Member

    Jun 4, 2004
    31
    0
    well i have used substitution method but i am unable to solve it correctly:'(
     
  5. haditya

    Senior Member

    Jan 19, 2004
    220
    0
    is the answer 7 -(5^1.5)/2
     
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