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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.

    symimage.cgi?expr=%20m%28b-a%29%20%3C%3D%20int_a%5Eb%20f%28x%29dx%20%3C%3D%20M%28b-a%29%20.gif

    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

    vela

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    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.
     
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