Estimating the value of an integral

[tangibleLime]

Homework Statement

It is known that if m[PLAIN]http://www.webassign.net/images/lteq.giff(x)[ATTACH=full]196966[/ATTACH]M for a[PLAIN]http://www.webassign.net/images/lteq.gifx[ATTACH=full]196967[/ATTACH]b, then the following property of integrals is true.

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

____________ <=

<= _____________

Homework Equations

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.

 

[vela]

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.