Results 1 to 2 of 2

Math Help - integral

  1. #1
    Banned
    Joined
    Dec 2008
    Posts
    15

    integral

    Evaluate the following integrals. z represent integral sign:-
    (a)
    Z xex dx.
    (b)
    Z x(4 + x2)^10 dx. (Hint: use the substitution u = 4 + x2.)

    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Dec 2008
    From
    Scotland
    Posts
    901
    Quote Originally Posted by trythis View Post
    Evaluate the following integrals. z represent integral sign:-
    (a)
    Z xex dx.
    (b)
    Z x(4 + x2)^10 dx. (Hint: use the substitution u = 4 + x2.)

    I'm sorry, what does the i represent in your first integral? Did you mean  \int xe^{x}dx ????

    If so use integration by parts!

     \int xe^x dx = [x \times \int e^x dx] - \int(( \int e^x dx) \times (\frac{d}{dx} x) dx)+C

      = [xe^x ] - \int e^x dx )+C

      = xe^x - e^x +C

      = e^x(x-1)+C

    For the second one:

     u = 4+x^2

    Hence

     \frac{du}{dx} = 2x

    Hence  \frac{1}{2}du = xdx

    Now you can replace your original integral :

     \int x(4+x^2)^{10} dx

    = \int (4+x^2)^{10} xdx

    = \int (u)^{10} \frac{1}{2}du

    = \frac{1}{2}\int (u)^{10} du

    You can do this, no? (remember to change back to original variable once you've integrated!)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: August 31st 2010, 07:38 AM
  2. Replies: 1
    Last Post: June 2nd 2010, 02:25 AM
  3. Replies: 0
    Last Post: May 9th 2010, 01:52 PM
  4. Replies: 0
    Last Post: September 10th 2008, 07:53 PM
  5. Replies: 6
    Last Post: May 18th 2008, 06:37 AM

Search Tags


/mathhelpforum @mathhelpforum