Results 1 to 2 of 2

Math Help - Evaluating Riemann integrals

  1. #1
    Junior Member
    Joined
    Jan 2010
    Posts
    60

    Evaluating Riemann integrals

    Let f(x)=2 if 0\leq x<1 and f(x)=1 if 1\leq x\leq 2 . Show that f\in R[0,2] and evaluate its integral.

    I'm not sure of the latex code for partitions...
    Last edited by frenchguy87; April 18th 2010 at 05:52 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Focus's Avatar
    Joined
    Aug 2009
    Posts
    228
    Quote Originally Posted by frenchguy87 View Post
    Let f(x)=2 if 0\leq x<1 and f(x)=1 if 1\leq x\leq 2 . Show that f\in R[0,2] and evaluate its integral.

    I'm not sure of the latex code for partitions...
    Which part do you need help on? The value of the integral is pretty clear (it's just two boxes, so calculate the area of the boxes).

    As for the integrability, try treating them as two functions g_1(x)=2\cdot\mathbf{1}_{[0,1)}(x) and g_2(x)=\mathbf{1}_{[1,2]}(x) where \mathbf{1}_A(x)=1 only when x \in A and is zero otherwise.

    When you show that both of those are integrable, then you know that the sum of them (which gives you f) is integrable.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: November 20th 2009, 09:30 AM
  2. evaluating integrals
    Posted in the Calculus Forum
    Replies: 2
    Last Post: July 23rd 2009, 05:51 PM
  3. Evaluating Integrals
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 14th 2008, 08:11 AM
  4. Evaluating Riemann Sum
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 10th 2007, 07:30 PM
  5. Riemann Sums and Riemann Integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 1st 2006, 01:08 PM

Search Tags


/mathhelpforum @mathhelpforum