Results 1 to 2 of 2

Math Help - Definite Integral

  1. #1
    Member RedBarchetta's Avatar
    Joined
    Apr 2008
    From
    United States
    Posts
    114

    Definite Integral

    1. The problem statement, all variables and given/known data

    \int_0^a {x\sqrt{x^2+a^2}\,dx}

    Also, (A>0)


    Firstly, I set

    u=x^2+a^2

    Then take the derivative,

    du=2x dx

    1/2\int_0^a {\sqrt{u}\,du}

    Now I integrated. So

    (1/3) * [(x^2+a^2)^3/2] from a to 0.

    I ended up with

    (1/3)[(a^2+a^2)^(3/2)-a^3]

    This is where I get lost. It must have something to do with the (A>0). The
    answer in the book is:

    (1/3)(2*sqrt(2)-1)a^3

    I can't see how to eliminate the a's to get the (2*sqrt(2)-1).

    Thanks for the help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    (1/3)[(a^2+a^2)^(3/2)-a^3]
    \frac{1}{3}\left[(a^2+a^2)^{3/2}-a^{3} \right]

    you are correct we just need to simplify.

    \frac{1}{3}\left[(2a^2)^{3/2}-a^{3} \right]

    \frac{1}{3}\left[2^{3/2}a^3-a^{3} \right]

    \frac{1}{3}\left[2\sqrt{2}a^3-a^{3} \right]

    \frac{1}{3}\left[2\sqrt{2}-1 \right]a^{3}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: December 5th 2011, 05:21 PM
  2. Replies: 4
    Last Post: April 13th 2011, 02:08 AM
  3. definite integral/ limit of integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 22nd 2010, 04:00 AM
  4. definite integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 1st 2008, 12:04 PM
  5. Definite integral ln(1+t)dt
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 26th 2008, 06:02 AM

Search Tags


/mathhelpforum @mathhelpforum