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Math Help - Basic Integration

  1. #1
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    Basic Integration

    Find the area between y=ln(x) and the x axis on the interval [1,e^2]

    I know how to integration, but is this possible? How would I integrate lnx?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Sm10389 View Post
    Find the area between y=ln(x) and the x axis on the interval [1,e^2]

    I know how to integration, but is this possible? How would I integrate lnx?
    one way, the most famous, is to integrate by parts. using u = ln(x) as the function you differentiate and dv = dx as the function you integrate

    ln(x) has actually been integrated several ways on this forum, it might do you good to do a quick search
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  3. #3
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    Ok so use 1 and lnx.

    My answer is xlnx-1

    is that right?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Sm10389 View Post
    Ok so use 1 and lnx.

    My answer is xlnx-1

    is that right?
    no
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  5. #5
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    maybe i just wrote it wrong

    u=ln(x)
    v'=1
    u'=1/x
    v= x

    =
    lnx*x - x(1/x)
    =
    (lnx) - 1

    Where is it wrong
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Sm10389 View Post
    maybe i just wrote it wrong

    u=ln(x)
    v'=1
    u'=1/x
    v= x

    =
    lnx*x - x(1/x)
    =
    (lnx) - 1

    Where is it wrong
    you have to integrate the second term according to the formula...

    \int \ln x ~dx = x \ln x - \int x \cdot \frac 1x~dx
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  7. #7
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    that is integrating... by parts.
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