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    I'm trying to find the ratio of the areas formed for the equation y=x^n, between x=0,1 and the x axis and y=0,1 and the y axis

    When it is:

    y=x^3

    the area i get for x is \frac{1}{4} and for y is \frac{3}{4}

    Ratio is then 3:1

    y=x^4

    the area i get for x is \frac{1}{5} and for y is \frac{4}{5}

    the ratio is then 4:1

    I speculate then that the ratio would be: n:1

    However, when I then test other real numbers like fractions/irrational numbers, it doesn't seem to work. What am I doing wrong?
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    1. Does the question say that n must be an integer (or might it be implied at the level of maths you are doing)?

    2. Did you use a calculator or not to work out the areas? (though I don't really see why it should make a difference)?
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    (Original post by LeeC)
    1. Does the question say that n must be an integer (or might it be implied at the level of maths you are doing)?
    It says 'calculate the ratio for y=x^n, nEZ (positive integers). But then it says 'test to see if this holds for other subsets of the real numbers'

    2. Did you use a calculator or not to work out the areas? (though I don't really see why it should make a difference)?
    I used a calculator and graphing software
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    Well then yeh you got the ratio for the positive integers, and no, it doesnt work for other subsets of the real numbers (at least the ones you've tried).
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    So my ratio of n:1 is right? but it doesn't work for other real numbers like fractions/irrational numbers. does it work for other real numbers?
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    Yeh if it works then it is right! I', sure you can check it for youself lol...but I wouldnt know about other real numbers at all...you would have to try different sets of reals (or ask somebody who knows more than me about this)
 
 
 
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Updated: November 9, 2008

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