Results 1 to 2 of 2

Math Help - Need urgent help! Integration in C0[0,1]

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    12

    Need urgent help! Integration in C0[0,1]

    Need urgent help with this problem.

    1)Let f be a function in C0[0,1] ie the space of continuous functions defined on the unit interval. Suppose that the Integral from 0 to 1 of the product of f and g (ie, f(x)*g(x) integrated from 0 to 1), for any g in C0[0,1] always vanishes. Prove that F is the constant zero function on [0,1].

    2) What if g is restricted to being of the form g(x)=x^n for some natural n?

    Many Many Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Feb 2010
    Posts
    147
    Quote Originally Posted by frederick111 View Post
    Need urgent help with this problem.

    1)Let f be a function in C0[0,1] ie the space of continuous functions defined on the unit interval. Suppose that the Integral from 0 to 1 of the product of f and g (ie, f(x)*g(x) integrated from 0 to 1), for any g in C0[0,1] always vanishes. Prove that F is the constant zero function on [0,1].

    2) What if g is restricted to being of the form g(x)=x^n for some natural n?

    Many Many Thanks!

    1) Consider g(x) = f(x)

    2) Use the fact that polynomials are dense in C0 to show that the Integral from 0 to 1 of the product of f and g (ie, f(x)*g(x) integrated from 0 to 1), for any g in C0[0,1] always vanishes, and just use the result from part 1).,
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Urgent Integration Help
    Posted in the Calculus Forum
    Replies: 16
    Last Post: February 5th 2009, 07:11 PM
  2. integration - urgent help please
    Posted in the Calculus Forum
    Replies: 10
    Last Post: November 4th 2007, 08:15 AM
  3. integration - urgent help please
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 28th 2007, 04:24 AM
  4. integration - urgent help please
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 17th 2007, 06:53 PM
  5. integration urgent help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 14th 2006, 06:32 AM

Search Tags


/mathhelpforum @mathhelpforum