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    Hmm... I think this is one of that \displaystyle \int_0^a f(x) dx = \int_0^a f(a-x) dx jobs

    (Original post by sonofdot)
    so then I would get xcosecx which I could do by parts, but I can't be bothered to do that now :p:
    Kinda tough integral though, doesn't evaluate in elementary functions
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    (Original post by SimonM)
    A little easy again

    Spoiler:
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    Based on two basic theorems

    \displaystyle \sum_{k=0}^{\infty} x^k = \frac{1}{1-x}
    and
    \displaystyle \sum_{k=0}^{\infty} kx^k = \frac{x}{(1-x)^2}

    Combining these we get

    \displaystyle \frac{a}{b} + \frac{a+c}{bd} + \frac{a+2c}{bd^2} + \frac{a+3c}{bd^3} + \cdots = \frac{a}{b} \sum_{k=0}^{\infty} \left ( \frac{1}{d} \right )^k + \frac{c}{b} \sum_{k=0}^{\infty} k \left ( \frac{1}{d} \right)^k = \frac{a}{b} \frac{1}{1-\frac{1}{d}} + \frac{c}{b} \frac{\frac{1}{d}}{(1-\frac{1}{d})^2} = \boxed{ \frac{ad}{b(d-1)} + \frac{c}{b} \frac{d}{(d-1)^2}}


    Random trivia: \begin{pmatrix} a \\ b \end{pmatrix} is not the same thing as \displaystyle \left( \frac{a}{b} \right). The latter is something called the Jacobi symbol.
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    (Original post by Zhen Lin)
    Random trivia: \begin{pmatrix} a \\ b \end{pmatrix} is not the same thing as \displaystyle \left( \frac{a}{b} \right).
    Doh
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    (Original post by SimonM)
    Hmm... I think this is one of that \displaystyle \int_0^a f(x) dx = \int_0^a f(a-x) dx jobs



    Kinda tough integral though, doesn't evaluate in elementary functions

    Yep that's the way forward (that's how the teacher expected us to do it atleast)
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    (Original post by SimonM)
    Hmm... I think this is one of that \displaystyle \int_0^a f(x) dx = \int_0^a f(a-x) dx jobs
    I must be being absolutely stupid, but isn't it:

     \displaystyle \int_0^a f(x) dx = - \int_0^a f(a-x) dx ?
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    (Original post by GHOSH-5)
    I must be being absolutely stupid, but isn't it:

     \displaystyle \int_0^a f(x) dx = - \int_0^a f(a-x) dx ?
    Nope
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    (Original post by GHOSH-5)
    I must be being absolutely stupid, but isn't it:

     \displaystyle \int_0^a f(x) dx = - \int_0^a f(a-x) dx ?
    Consider the substitution  y = a - x and the fact that  \int_0^a f(x) dx = - \int_a^0 f(x) dx
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    (Original post by Hancock orbital)
    Consider the substitution  y = a - x and the fact that  \int_0^a f(x) dx = - \int_a^0 f(x) dx
    im an idiot. thank you.
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    (Original post by Hancock orbital)
    Consider the substitution  y = a - x and the fact that  \int_0^a f(x) dx = - \int_a^0 f(x) dx
    im an idiot. thank you.
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    [joke]
    if we define "one" as "two" and "two as "one" does that gives "two plus two equals one"?
    [/]

    anyway, join request on the way
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    (Original post by ~|Shock|~)
    [joke]
    if we define "one" as "two" and "two as "one" does that gives "two plus two equals one"?
    [/]

    anyway, join request on the way
    NO
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    (Original post by Ekpyrotic)
    Ok, I understand it's customary to post a problem. Might be a little old but it's a good 'un.

    ABC is isosceles.

    AB=BC

    AB= \sqrt 5

    AC=2

    Find a way to cut the triangle into 4 pieces so that they can be constructed to form a regular square.
    I must be some sort of idoit but can someone put a hint?


    Another problem, though not very mathys:

    A farmer has the following three fields and he has 4 sons and 4 daughters. He wants to leave them with land when he passes away and to be fair they all have to have the same size plot and same shape plot. How can this be achieved?

    Attached Images
     
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    (Original post by The Muon)
    A farmer has the following three fields and he has 4 sons and 4 daughters. He wants to leave them with land when he passes away and to be fair they all have to have the same size plot and same shape plot. How can this be achieved?
    Does the solution involve molesting his eldest daughter to acquire a ninth child? It's plausible; you know what farmers are like :jiggy:. I think. *ahem*.
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    (Original post by The Muon)
    I must be some sort of idoit but can someone put a hint?


    Another problem, though not very mathys:

    A farmer has the following three fields and he has 4 sons and 4 daughters. He wants to leave them with land when he passes away and to be fair they all have to have the same size plot and same shape plot. How can this be achieved?

    How about leaving one field for animals to graze upon, and dividing the remaining two fields into equally sized squares and give them to his children?
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    (Original post by Mathematician!)
    How about leaving one field for animals to graze upon, and diving the remaining two fields into equally sized squares and give them to his children?
    I do not know the answer, it's on the wall at college and I can never figure it out.
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    (Original post by The Muon)
    I do not know the answer, it's on the wall at college and I can never figure it out.
    Well this is plausible, as it doesn't say you can't leave a field for animals :p:
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    (Original post by DeanK22)
    Have not drawn this out just thought about in my head but;

    Spoiler:
    Show
     24 \div  3 = 8 and  24 \times 3 = 72

     72 \div 8 = 9


    Spoiler:
    Show
    Chop each square into 24 rectangles allocating 2 rectangles from the big square and 1 from the square beneath, alternating this pattern. Consider the rectangle at the left with nothing above or below. Give three rectangles to one person.


    Should do it - everbody gets  9 rectangles.
    Off topic, but did DeanK2 get a perm. ban?
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    (Original post by DeanK22)
    This is the same person :rolleyes: ...
    No really? :rolleyes:

    What I meant is did your other account get a perm. ban?
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    (Original post by DeanK22)
    I requested such a ban due to spending too much time on TSR - the irony.
    Lol! Why did you start a new account then? :eyeball:
    Changed your mind?
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    (Original post by Mathematician!)
    Lol! Why did you start a new account then? :eyeball:
    Changed your mind?
    TSR was the cause for quite literally doing nothing in terms of school work and I thought this would have affected my exams (considering I had done no homework in any of my subjects) and I need three a for Oxford. Considering how my exams have recently gone though I found that you can quite literally learn whole modules in one or three days - subject specific - ergo TSR time.

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