Results 1 to 3 of 3

Math Help - riemann sums and definite integral represeting are of region

  1. #1
    Junior Member
    Joined
    Jun 2008
    From
    tucson, az
    Posts
    31

    riemann sums and definite integral represeting are of region

    I have to find the remain sum the the integral of the area between the curves of y=x and y=sqrt(x) with horizontal slices. not sure how to do it, i know it would be the area under y=sqrt(x) minus the area under y=x but not sure how to do it. Thanks for the help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member arpitagarwal82's Avatar
    Joined
    Feb 2009
    Posts
    103
    If you solve both equation, you will get the points of intersection as (0,0) and (1,1)

    Now So simply integrate  \int (\sqrt(x) - x )dx with in limit x = 0 to  x= 1
    Attached Thumbnails Attached Thumbnails riemann sums and definite integral represeting are of region-01.jpg  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member arpitagarwal82's Avatar
    Joined
    Feb 2009
    Posts
    103
    And yes, above solution was for verticle slices. For horizontal slices you have to integrate with respect to y.
    So integrate y - y^2 wrt y with in same limits y = 0 to y= 1
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] definite integral that gives area of a region
    Posted in the Calculus Forum
    Replies: 12
    Last Post: October 20th 2011, 10:58 PM
  2. Help with Riemann Sums and Definite Integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 7th 2010, 06:24 AM
  3. Replies: 7
    Last Post: May 21st 2010, 04:57 AM
  4. Replies: 1
    Last Post: November 19th 2009, 11:10 PM
  5. adding sums, definite integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 29th 2009, 03:10 PM

Search Tags


/mathhelpforum @mathhelpforum