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    I want to find the area in the upper right quadrant within the curve y^m + x^(4-m) = 1, where me takes values between 0 and 4.

    Any ideas how do I go about this? I'm sure exotic functions will be involved... I am open to this.
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    did you try WA?
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    Wolfram says:

    \displaystyle \frac{\Gamma (\frac{1}{4 - t}) \Gamma( \frac{1}{t}) }{4 \Gamma(\frac{4}{4t-t^2})}

    But I haven't actually looked at actually working it out.

    Thoughts:

    Products of gamma functions - use x \to \sqrt{x} to obtain something like that integral for \int e^{-x^2}
    :Doesn
    It worked. (I'll write it up as soon as I get the chance, currently sharing a computer)


    What's the context of this problem?
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    thanks. write up would be appreciated actually.

    the context is actually real world - it comes up in new insurance regulation, believe it or not.
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    If problems like this are frequent in your work, I'm sure your employer could afford a licence for Mathematica.
 
 
 
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