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Family of Curves

  1. Jan 1, 2010 #1
    f I consider the area of the family of curves as y = (1 - x^1/p)^n where x is greater than or equal to zero but less than or equal to one, I can write that in as integral as

    the integral from 0 to 1 of (1 - x^1/p)^n dx but I'm not sure how to write that as a summation, which I have been trying to do. I know the summation looks like:

    summation from k=0 to n ((-1)^k (n k) p/(p+k))

    Can you please help me with this?
  2. jcsd
  3. Jan 1, 2010 #2


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    I am confused (although it looks like to me you are confused) as to what your summation is supposed to represent.

    First you talk about a family of curves. What is the parameter defining the family (n or p)?

    The you talk about an integral over x, but p and n seem to be fixed.

    Finally what are you using the sum for? Are you representing the integral as a sum? It doesn't look like that at all.
  4. Jan 1, 2010 #3
    My summation as well as the integral is supposed to represent the area under the curve.

    n and p are just positive integers. I need to figure out how the area under the curve can be written as the integral equal to the summation.
  5. Jan 2, 2010 #4


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    The area under what curve? You have, as you said, a family of curves and each curve in that family has a different area. Certainly, summing over n will NOT give you the area under any curve.
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