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Thread: ratio of two definite Integration

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    ratio of two definite Integration


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    Junior Member BenHowe's Avatar
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    Re: ratio of two definite Integration

    I think I know how to do this although my answer is pretty disgusting (could be wrong). I don't know how to use latex so I'll just tell you what I did.

    So since the integrals have the same limits and variable, if you write the integral of I/J, its the same as finding the values of I and J and then dividing it. When you re-write the integral the (1-x)^7/2 terms cancel out and the x^5/2 is just reduced to x. So you're left with x(3+x)^8. Then it's just a sub for 3+x and bob's your uncle.
    1st Year BAppFinBActStud @ MQ

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    Supreme Member seanieg89's Avatar
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    Re: ratio of two definite Integration


    in general.

    Eg let a=0, f(x)=x^2, g(x)=x.
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    Junior Member BenHowe's Avatar
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    Re: ratio of two definite Integration

    Oh. Man I just tried to type up my solution in LaTex for the 1st time but I didn't know how to put it as text in the document only as a picture. How do I put it as text like the posts above (even though ik it's wrong now -_- )
    Last edited by BenHowe; 14 Feb 2017 at 9:46 AM.
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    Re: ratio of two definite Integration

    Sorry friends actually original question as


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    -insert title here- Paradoxica's Avatar
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    Re: ratio of two definite Integration

    Quote Originally Posted by juantheron View Post
    Sorry friends actually original question as

    The answer is very simple.



    The remainder of the problem is trivial.
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    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

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    I love trials pikachu975's Avatar
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    Re: ratio of two definite Integration

    Quote Originally Posted by Paradoxica View Post
    The answer is very simple.



    The remainder of the problem is trivial.
    Can I ask how'd you get u = 4x/(x+3)?
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    -insert title here- Paradoxica's Avatar
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    Re: ratio of two definite Integration

    Quote Originally Posted by pikachu975 View Post
    Can I ask how'd you get u = 4x/(x+3)?
    A rational substitution of the form u = A + B/(x+3) will take out (x+3)^2 from the denominator, simply by existing. That is the primary purpose of the substitution. The remaining part of the denominator can be perfectly repartitioned across the two components of the denominator.

    The secondary purpose is to pick such coefficients A and B such that the borders coincide, which can be done by substituting values.

    The third purpose is to make it such that the integral is exactly transformed into a constant multiple of I, which just so happens to be possible because of the way this problem was designed. For arbitrary problems, such a transformation may not be possible.

    It only took a few minutes of scribbling until I was done with the problem, at least intuitively, and the details were fleshed out while typesetting.
    Last edited by Paradoxica; 3 Apr 2017 at 12:06 AM.
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    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

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