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Definite Integrals

  1. Aug 16, 2007 #1
    1. The problem statement, all variables and given/known data

    Evaluate the definite integrals.

    2. Relevant equations

    Integral of (t+1)/(t^2+2t+1) dt from 1 to 4 (a=1, b=4)

    and

    Integral of (xe^(x^2+1)) dx from 0 to 2 (a=0, b=2)


    3. The attempt at a solution

    I have done them out, just wondering if this is the best way to do them, and perhaps if I made a mistake, it would be nice to know why:

    For the first one, I factored and got:

    (t+1) / ((t+1)(t+1))

    then i cancelled and got

    1 / (t+1)

    Which then means:

    ln |t+1| from 1 to 4 = ln |5| - ln |2|

    Is that the answer for that?




    Now, for the second one, I did the same thing:

    antiderivative of (xe^(x^2+1)) = 1/2 (e^(x^2+1)...

    right? Then the answer would be from 0 to 2:

    e^5 - e^1 = e^4

    Any feedback would be great.
     
  2. jcsd
  3. Aug 16, 2007 #2
    That's right.

    Nope. For one, you forgot the factor of 1/2 in front, and also e^a - e^b is not equal to e^(a-b) [actually, that's true for any base.]

    The first one's right, BTW.
     
  4. Aug 16, 2007 #3
    Thanks.

    So if I did the second correctly, it's:

    1/2 e^5 - e/2

    Right? And I can leave it like that?
     
  5. Aug 16, 2007 #4

    learningphysics

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    Homework Helper

    Yes, looks fine.
     
  6. Aug 16, 2007 #5
    If you mean, [tex]\frac{1}{2}e^5 - \frac{1}{2}e[/tex], then that's right, although [tex]\frac{1}{2}\left(e^5 - e\right)[/tex] would look nicer. :)
     
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