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    I'm not asking you to do it for me (unless you want to:p: ), but i just dont know what to do, so what would you do..?

    Heres the Q:

    For the function y=x^n, the ratio of area A:Area B is n:1, where A is the area from y = 0 to 1 and the y axis, and B is the area from x = 0 to 1 and the x axis. As shown:


    Is this ratio true for the general case y=x^n from x = a to b such that a < b, and for the regions defined below?

    Area A: y=x^n, y=a^n, y=b^n and the y axis
    Area B: y=x^n, x = a, x=b and the x axis

    If so prove it; if not why not?

    ___

    Once again, I'm not asking you to do it for me, I just need help as to what to do

    I've proven that the ratio holds for like x = 0 to 5, or 2 to 7, but what else do i need to do?/ What is the question really asking for
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    i would wager a guess at do the intergral for 0 1 of both, then one with intergrals infinite, this is just a guess atm.
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    I'm guessing just do an integral to find an area (for arbitrary n) and then subtract from total area of box to get other area.
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    I think I should also be looking at negatives as well (not just Quadrant I), but not sure...

    i would wager a guess at do the intergral for 0 1 of both, then one with intergrals infinite, this is just a guess atm.
    How would i do that infinite thing?

    I'm guessing just do an integral to find an area (for arbitrary n) and then subtract from total area of box to get other area.
    Ye I did that so i have an equation to get the area of A and B when I plug in the n value, but not sure how to continue
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    (Original post by G O D I V A)
    Ye I did that so i have an equation to get the area of A and B when I plug in the n value, but not sure how to continue
    Erm, at this point, check the ratio.

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    Divide your formula for the area of A by the area of B. That gives you the ratio. Check if the ratio is always n:1 for any choice of a, b and n, or (the negation) that there exists some choice of a, b, n where the ratio is not n:1.
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    Integrating from a to b (both positive) it would be, b-a

    If a and b are both negative, is it (-b)-(-a)? or (-a)-(-b)

    If b is positive and a is negative it is b-(-a) ??
 
 
 
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Updated: November 16, 2008

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