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Math Help - integration problem

  1. #1
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    integration problem

    this is a L-R Series Circuit with
    V= 240 cos 10t
    R= 100 Ohm
    L= 20 Henry

    It asks to find current in circuit at any time if initially there is no current.

    this is from my lecture notes so there is a step im not sure how to get.
    d/dt(ie^5t) = 12 e^5t cos 10t
    ie^5t = 12 ∫e^5t cos 10t dt
    = 12/25 e^5t [cos 10t + 2sin 10t] +c

    how do i integrate e^5t cos 10t to get to the next step?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by yen yen View Post
    this is a L-R Series Circuit with
    V= 240 cos 10t
    R= 100 Ohm
    L= 20 Henry

    It asks to find current in circuit at any time if initially there is no current.

    this is from my lecture notes so there is a step im not sure how to get.
    d/dt(ie^5t) = 12 e^5t cos 10t
    ie^5t = 12 ∫e^5t cos 10t dt
    = 12/25 e^5t [cos 10t + 2sin 10t] +c

    how do i integrate e^5t cos 10t to get to the next step?
    you can use integration by parts. do you remember the formula?

    Let u=\cos 10t and dv = e^{5t}~dt

    Find du and v and use the formula: \int u~dv = uv - \int v~du
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    you can use integration by parts. do you remember the formula?

    Let u=\cos 10t and dv = e^{5t}~dt

    Find du and v and use the formula: \int u~dv = uv - \int v~du
    this is the one derived from the product rule for differentiation right?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by yen yen View Post
    this is the one derived from the product rule for differentiation right?
    that's correct. we use it to integrate products (where possible)
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