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Math Help - definite integrals

  1. #1
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    definite integrals

    if anyone can help me with this, that would be great!
    this is from ln3 to ln2
    ∫ 3/(e^(3t)) dt=???
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  2. #2
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    Quote Originally Posted by gearshifter View Post
    if anyone can help me with this, that would be great!
    this is from ln3 to ln2
    ∫ 3/(e^(3t)) dt=???
    use the formula \int e^{at} ~dt= \frac{1}{a}e^{at}
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  3. #3
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    what do I do with the 3 on top?
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  4. #4
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    Quote Originally Posted by gearshifter View Post
    if anyone can help me with this, that would be great!
    this is from ln3 to ln2
    ∫ 3/(e^(3t)) dt=???
    If you are not getting what the above post says:

    let u = 3t

    then,  du = 3 dt

    so, dt= \frac{du}{3}

    so you have

    \int_{ln3}^{ln2} {3 e^{-u}}\frac{du}{3}

    = [-e^{-u}]_{ln3}^{ln2}

    substitute u = 3t, you get

    [-e^{-3t}]_{ln3}^{ln2}

    calculate the value for the given upper and lower limits
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