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Integration by Parts Watch

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    Can someone help with this? No idea how to do the first part. I've attached my working out so far.

    Attachment 694372694374
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    (Original post by hatedigi)

    Can someone help with this? No idea how to do the first part. I've attached my working out so far.
    You seem to be saying that the derivative wrt t of t^x is 1 but I'm not sure why?
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    (Original post by Notnek)
    You seem to be saying that the derivative wrt t of t^x is 1 but I'm not sure why?
    nvm, how would I differentiate it with respect to t then?
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    (Original post by hatedigi)
    nvm, how would I differentiate it with respect to t then?
    Treat x as a constant so you can differentiate it just like you would differentiate t^3 for example.
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    (Original post by Notnek)
    Treat x as a constant so you can differentiate it just like you would differentiate t^3 for example.
    Ok so this is what I have now but I have an extra - e ^ -t * t^ xName:  image.jpg
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    (Original post by JustChilling24/7)

    Maybe this will help for the first part
    I had to remove your post unfortunately because it contained a full solution which is against the maths forum rules. It would be great if you can help the OP at the point they are stuck without giving a solution.

    I won't be able to help until later.
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    (Original post by Notnek)
    I had to remove your post unfortunately because it contained a full solution which is against the maths forum rules. It would be great if you can help the OP at the point they are stuck without giving a solution.

    I won't be able to help until later.
    Oops I did not know that sorry my bad.
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    Try to integrate gamma(x) instead of gamma(x+1)
    (Original post by hatedigi)
    Ok so this is what I have now but I have an extra - e ^ -t * t^ xName:  image.jpg
Views: 13
Size:  489.2 KB
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    (Original post by JustChilling24/7)
    Try to integrate gamma(x) instead of gamma(x+1)
    Still got a term at the front getting in the way unfortunately Name:  image.jpg
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    (Original post by hatedigi)
    ...
    When using integration by parts on a definite integral you need to evaluate the term you've separated out at the two limits of the integral.


    e^{-t}t^x

    should be more correctly written as:

    \displaystyle \left[e^{-t}t^x\right]_0^{\infty}
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    You need to evaluate your [e-t tx] between infinity and zero (this is integration by parts). You should notice something happen to this expression when you sub in the limits.
    (Original post by hatedigi)
    Still got a term at the front getting in the way unfortunately Name:  image.jpg
Views: 13
Size:  497.0 KB
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    It seems like you're struggling to deal with infinite limits, as they aren't taught at A level.
     \displaystyle \int_{0}^{\infty}{F(t)}dt = lim_{u \rightarrow \infty} [f(t)]_{0}^{u} , where F(t) is the derivative of f(t), in this case the limit exists so there will be a convergence; just consider what factor grows faster?

    I remember finding a good explanation of this if you Google "Paul's math notes".
 
 
 
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