1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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)


    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

    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


    User Avatar
    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. :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook