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Math Help - Integral Problem

  1. #1
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    Integral Problem

    Hi, I am having some trouble with this integral problem,



    I believe it is integration by parts. I don't know the "[m@th][/m@th]" tags so if someone could point me to a link that would be great too.
    Thanks,
    Matt
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    Quote Originally Posted by matt3D View Post
    Hi, I am having some trouble with this integral problem,



    I believe it is integration by parts.
    Thanks,
    Matt
    yes, integration by parts.

    let u = t (the part you differentiate) and dv = e^{-t}~dt

    can you take it from here?
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  3. #3
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    I get stuck after -te^-t - int from 0 to 2 -e^-t dt
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by matt3D View Post
    I get stuck after -te^-t - int from 0 to 2 -e^-t dt
    stuck with what? finding \int_0^2-e^{-t}~dt?
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    Quote Originally Posted by Jhevon View Post
    stuck with what? finding \int_0^2-e^{-t}~dt?
    Yea!
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by matt3D View Post
    Yea!
    i am really surprised by this

    you manage to do \int e^{-t}~dt but you can't do \int-e^{-t}~dt? i don't get you

    Note that \int-e^{-t}~dt = - \int e^{-t}~dt which you know how to find, because you did it already

    is it the limits that are bothering you? you know how to use the fundamental theorem of calculus?
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  7. #7
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    Okay, I get -te^{-t}-\int_0^2-e^{-t}~dt
    And I am stuck with the new integral to the right. Yes, I do know the fundamental theorem of calculus. Could you just show me the steps to the whole problem? I really appreciate your time and help.
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    Quote Originally Posted by matt3D View Post
    Okay, I get -te^{-t}-\int_0^2-e^{-t}~dt
    And I am stuck with the new integral to the right. Could you just show me the steps to the whole problem? I really appreciate your time and help.
    you're lucky i have to leave now, so i can't spend the time having you work things out

    \int_0^2 te^{-t}~dt = -te^{-t} - \int_0^2 -e^{-t}~dt

    = -te^{-t} + \int_0^2 e^{-t}~dt

    = -te^{-t} - e^{-t} \bigg|_0^2

    = -(t + 1)e^{-t} \bigg|_0^2

    = -(2 + 1)e^{-2} - [-(0 + 1)e^0] .............by the fundamental theorem of calculus

    = -3e^{-2} + 1
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  9. #9
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    Thank you so much!
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  10. #10
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    Quote Originally Posted by matt3D View Post
    I don't know the "[m@th][/m@th]" tags so if someone could point me to a link that would be great too.
    Thanks,
    Matt
    see here
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