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Integration of e^(y^3)

  1. Apr 3, 2010 #1
    The function i need to integrate is

    [tex]\displaystyle\int^3_0 \int^1_{\sqrt{\frac{x}{3}}} e^y^3,dydx[/tex]

    however my problem is integrating:
    [tex]\int^1_{\sqrt{\frac{x}{3}}} e^y^3 dy[/tex]

    I have looked on the forum and everyone is mentioning erf(x) which i dont understand yet. Do i need this for this definite integral? If so where can i learn about it and how to use it?
  2. jcsd
  3. Apr 3, 2010 #2


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    Try changing the order of integration.

    For this integral, x ranges from 0 to 3 and, for each x, y from [itex]\sqrt{x/3}[/itex].

    When x= 3, [itex]y= \sqrt{x/3}= 1[/itex] and when x= 0, [itex]y= \sqrt{0/3}= 0[/itex] so y ranges from 0 to 1. For each y, since [itex]y= \sqrt{x/3}[/itex] leads to [itex]y^2= x/3[/itex] or [itex]x= 3y^2[/itex], x ranges from 0 to 3y^2. Try
    [tex]\int_{y= 0}^1 \int_{x= 0}^{3y^2} e^{y^3} dx dy[/tex]
  4. Apr 3, 2010 #3
    that actually worked out quite nicely. Thank you.
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