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How to integrate this?

  1. Oct 3, 2008 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
    I've been wondering about the correct way to deal with this type of integral for quite a long time. To me, the above integral looks like something of the form:
    n appears in the integrand AND in the limits of integration, how can I integrate in this case?

    I am just wondering whether n can be treated as a "constant" in the above integral, i.e. can I treat 2^n as a constant and pull the 2^n OUT of the integral and evaluate
    ∫2-tdt ?

    Thank you for explaining!
  2. jcsd
  3. Oct 3, 2008 #2


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    Yes, the n is a constant in this case.
  4. Oct 3, 2008 #3


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    First, 2n-t= 2n 2-t.

    Second, the derivative of 2t is (ln 2)2t so the anti-derivative is 2t/ln(2).
  5. Oct 3, 2008 #4
    So even though "n" appears in the integrand and also appears in the limits of integration, we can still treat the "n" in the integrand as a constant and use the property ∫cf(t)dt=c∫f(t)dt ?
    Last edited: Oct 3, 2008
  6. Oct 3, 2008 #5


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    If you integrating with respect to t, you don't have to worry about anything else unless n is a function of t, which it is not stated to be.
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