Compute the upper and lower Riemann sums and the integral from zero to 1 of f(x)dx, where the partition is

P= {0, 2/5, 1/2, 3/5, 1}

Thanks.

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- Nov 6th 2007, 07:14 PMtaypezUpper and Lower Riemann Sums
Compute the upper and lower Riemann sums and the integral from zero to 1 of f(x)dx, where the partition is

P= {0, 2/5, 1/2, 3/5, 1}

Thanks. - Nov 6th 2007, 08:11 PMThePerfectHacker
- Nov 7th 2007, 04:34 AMtaypez
f(x) = 1-x^2

- Nov 7th 2007, 05:52 AMkalagota
$\displaystyle f(x) = 1 - x^2$

f(x) is decreasing from 0 to 1. hence, for the given partition:

$\displaystyle U(P,f) = 1\cdot \frac{2}{5} + \frac{21}{25} \cdot \frac{1}{10} + \frac{3}{4} \cdot \frac{1}{10} + \frac{16}{25} \cdot \frac{2}{5} = \frac{163}{200}$

$\displaystyle L(P,f) = \frac{21}{25} \cdot \frac{2}{5} + \frac{3}{4} \cdot \frac{1}{10} + \frac{16}{25} \cdot \frac{1}{10} + 0 \cdot \frac{2}{5} = \frac{19}{40}$ - Nov 7th 2007, 09:42 AMtaypez
Can you give me an example of a couple calculations on how you arrived at these numbers for U(f,P)? I came up with some different ones and I can't find my mistake.

Thanks. - Nov 7th 2007, 09:44 AMThePerfectHacker