1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Estimating the value of an integral

  1. Sep 19, 2010 #1
    1. The problem statement, all variables and given/known data
    It is known that if m[PLAIN]http://www.webassign.net/images/lteq.giff(x)[ATTACH=full]196966[/ATTACH]M [Broken] for a[PLAIN]http://www.webassign.net/images/lteq.gifx[ATTACH=full]196967[/ATTACH]b, [Broken] then the following property of integrals is true.


    Use this property to estimate the value of the given integral.

    ____________ <= symimage.cgi?expr=%20int_0%5E1%205%2F%281%2Bx%5E2%29dx%20.gif <= _____________

    2. Relevant equations

    3. The attempt at a solution
    Honestly, I don't really know what it wants for a solution. I put in two numbers that satisfied the inequality, but it marked it wrong, so I assume it wants some sort of expression. The value of the integral itself is 5pi/4, but other than that I am at a complete loss for how to even begin.

    Nevermind, I figured it out... I was overcomplicating it. I didn't realize they were using M and m as a function... I thought they were multiplying it. So m(1) <= 5/(1+1^2) = 5/2, and so-forth.
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 19, 2010 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    They were multiplying it. Over the interval [0,1], the function 5/(1+x2) attains a maximum at x=0 and a minimum at x=1, so you can use the values m=f(1) and M=f(0) in the inequality.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook