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Calculus

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Find the indefinite integral

(integral sign) 3te^2tdt

  • Calculus -

    use a calculator, that's what calculus is all about. duh!

  • Calculus -

    Excuse you that DUH is not necessary and if I could use the calculator I would have used it but my teacher did not teach me to how to use the calculator for this so please mind your business

  • Calculus -

    do t e^(2t) dt
    and multiply by 3 later
    by parts
    u = t
    du = dt
    dv = e^(2t) dt
    v = (1/2) e^(2t)
    u v = (1/2) t e^(2t)
    v du = (1/2)e^(2t) dt
    integral v du = e^(2t)
    u v - integral v du = (1/2) t e^(2t) -e^(2t)

  • Calculus -

    then multiply by 3

  • Calculus -

    integral(u dv) = uv - integral(v du)

    let u = 3t
    du/dt = 3 , so du = 3 dt

    let dv = e^(2t)dt
    v = (1/2)e^(2t)

    so integral(3t(e^(2t)))dt = 3t(1/2)e^(2t) - integral((1/2)e^(2t)(3 dt)

    = (3/2)te^(2t) - (3/4)e^(2t)

    I don't know how much further you want to simplify this, but I differentiated my last answer and it works

  • Calculus -

    Let 3t = u and e^2t dt = dv
    du = 3 dt v = (1/2) e^2t
    The integral is
    uv - INTEGRAL v du
    = (3/2)t e^2t - INTEGRAL (3/2)e^2t
    = (3/2)t e^2t - (3/4)e^2t

  • Calculus -

    Thank You Damon, Reiny and Drwls for your help

  • Calculus -

    but why does v=(1/2)e^2t

  • Calculus -

    all three of us had chosen

    let dv = e^(2t)dt
    or dv/dt = e^(2t)

    wouldn't you have to integrate that to get v ?

    v = (1/2)e^(2t)

    I hope you recognized that we used a method called integration by parts

    in choosing the "u" and "dv"

    let u be something that you can differentiate, and
    let dv be the part that you can integrate,
    then hope for the best

  • Calculus -

    because d/dt of e^2t = 2 e^2t
    so you need the (1/2) to get one of them instead of 2

  • Calculus -

    oooo okay Thank You

  • Calculus -

    yeah you better say thank you and if i were to mind my own business then why did you post a question where everyone can see dufus?

  • Calculus -

    Ummm because I wasn't looking for help from you and of course I'm going to say Thank You because i have manners unlike you you don't have any and you don't address people that's looking for help form you like that so Goodbye and Have a nice day

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