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Math Help - change of variable for multiple integration. no known transformation.

  1. #1
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    change of variable for multiple integration. no known transformation.

    I am trying to find a transformation that will convert the region bounded by y=0 and y=(1+x^6)^1/6 to a region that is a rectangle.
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  2. #2
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    On what interval?
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  3. #3
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    The point is that those two curves do NOT bound a finite region.
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    Okay I cannot write things down. The second curve is y=(1-x^6)^1/6 so it bounds on x between -1 and 1 and y between 0 and 1. But I cannot integrate most functions with the above expression as a bound on my finite integral.
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  5. #5
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    If you're trying to transform the region bound by

    y = 0,  y = (1+x^6)^{1/6}, x = -1 \; \text{and}\; x = 1

    to say a rectangle, try the transformation

    u = x,\;\;  v = \dfrac{y}{(1+x^6)^{1/6}}.
    Last edited by Jester; December 16th 2010 at 06:16 AM. Reason: fixed sign problem
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