# using Property of Integral to estimate the value

• Nov 19th 2009, 01:59 PM
racewithferrari
using Property of Integral to estimate the value
• Nov 19th 2009, 02:08 PM
Plato
racewithferrari,
That is a good question.
What have you done to solve it?
I know you don't expect us to simlpy do it for you. Do you?
• Nov 19th 2009, 02:12 PM
racewithferrari
I miss my class when teacher was teaching it. Other than that I learned how to solve integrals by myself from the book. But this thing confuses me.
• Nov 19th 2009, 02:14 PM
lvleph
Well, the hardest part of this problem is determining m and M. However, we have an interval in which the function is non-increasing, [0,3]. So we know $\displaystyle f(3) \le f(x) \le f(0)$. From this we see that
$\displaystyle \frac{3}{1+3^2} \cdot (3 - 0)\le \int_0^3 \! \frac{3}{1 + x^2}\, dx \le \frac{3}{1+0^2} \cdot (3-0)$
$\displaystyle \frac{9}{10}\le \int_0^3 \! \frac{3}{1 + x^2}\, dx \le 9$
• Nov 19th 2009, 02:37 PM
racewithferrari
can u actually tell me what will be in the two boxes

thanks(Clapping)
• Nov 19th 2009, 02:40 PM
Plato
Quote:

Originally Posted by racewithferrari
can u actually tell me what will be in the two boxes

I do not understand why you expect complete answers.
• Nov 19th 2009, 02:43 PM
lvleph
Based on the way I did it, the boxes would be 9/10 and 9, respectively.