Results 1 to 2 of 2

Math Help - Odd and Even functions

  1. #1
    Senior Member
    Joined
    Jul 2009
    From
    Singapore
    Posts
    338

    Odd and Even functions

    Prove that:
    a) if f(x) is an even function, \int^a_{-a}f(x)dx=2\int^a_0 f(x)dx
    b)if f(x) is an odd function, \int^a_{-a} f(x)dx=0

    I tried using proof by contradiction:
    f(x) is even, then \int^a_{-a}f(x)dx\neq 2\int^a_0 f(x)dx
    My problem is I don't know how to continue.
    I figure if I get the first one right I can do the other.
    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    You have to use the conditions on even and odd functions. I would then break up both LHS integrals into two pieces: one on either side of the origin.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: April 15th 2010, 05:50 PM
  2. Replies: 3
    Last Post: February 23rd 2010, 04:54 PM
  3. Replies: 11
    Last Post: November 15th 2009, 11:22 AM
  4. Replies: 7
    Last Post: August 12th 2009, 04:41 PM
  5. Replies: 1
    Last Post: April 15th 2008, 09:00 AM

/mathhelpforum @mathhelpforum