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Math Help - Integration bt parts help

  1. #1
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    Exclamation Integration bt parts help

    1. The problem statement, all variables and given/known data

    Estimate  \int_{0}^{10} f(x) g'(x) dx   for f(x) = x^{2}
    and g has the values in the following table.

    <br />
      \begin{array}{l | c|c|c|c|c|c |} <br />
      \hline<br />
      \hline g&0&2&4&6&8&10\\<br />
      \hline g(x)&2.3&3.1&4.1&5.5&5.9&6.1\\<br />
      \hline<br />
      \end{array}<br />



    2. Relevant equations

     \int uv' dx = uv = \int u'v dx


    3. The attempt at a solution

    Okay so, since f(x) is x squared i chose

    u = x^{2} and v' = g'(x)
    &
    u' = 2x dx and v = g(x)

    plugging in...

    g(x)x^{2} -  \int_{0}^{10} 2xg(x) dx

    and this is where im stuck. I cant plug in the g values because i first need to take the integral of 2xg(x) ....I think. lol

    a nudge in the right direction would be ub3r helpful and much appreciated. thanks!

    ps. that latex table took me like a half hour to figure out rofl
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by spatran029 View Post
    1. The problem statement, all variables and given/known data

    Estimate  \int_{0}^{10} f(x) g'(x) dx   for f(x) = x^{2}
    and g has the values in the following table.

    <br />
      \begin{array}{|l | c|c|c|c|c|c |} <br />
          \hline g&0&2&4&6&8&10\\<br />
      \hline g(x)&2.3&3.1&4.1&5.5&5.9&6.1\\<br />
      \hline<br />
      \end{array}<br />



    2. Relevant equations

     \int uv' dx = uv = \int u'v dx


    3. The attempt at a solution

    Okay so, since f(x) is x squared i chose

    u = x^{2} and v' = g'(x)
    &
    u' = 2x dx and v = g(x)

    plugging in...

    g(x)x^{2} -  \int_{0}^{10} 2xg(x) dx

    and this is where im stuck. I cant plug in the g values because i first need to take the integral of 2xg(x) ....I think. lol

    a nudge in the right direction would be ub3r helpful and much appreciated. thanks!
    use by parts again to integrate the 2xg(x)

    ps. that latex table took me like a half hour to figure out rofl
    haha, good job!

    (i fixed it up a bit)
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    use by parts again to integrate the 2xg(x)
    but when i use v' = g(x) i dont know what v is.

    and if i use u = g(x) and v' = 2x i end up wher i started. LOL
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by spatran029 View Post
    but when i use v' = g(x) i dont know what v is.

    and if i use u = g(x) and v' = 2x i end up wher i started. LOL
    just write it as \int g(x)~dx. you can get as estimate for this integral using the table.
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  5. #5
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    oh right!! because were not looking for an exact value! thanks for helping me
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