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- Nov 19th 2009, 01:59 PMracewithferrariusing Property of Integral to estimate the value
- Nov 19th 2009, 02:08 PMPlato
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 PMracewithferrari
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 PMlvleph
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 PMracewithferrari
can u actually tell me what will be in the two boxes

thanks(Clapping) - Nov 19th 2009, 02:40 PMPlato
- Nov 19th 2009, 02:43 PMlvleph
Based on the way I did it, the boxes would be 9/10 and 9, respectively.