Limit of Riemann sums

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November 16th 2012, 02:30 PM
nubshat

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Limit of Riemann sums

Express the following integral as the limit of Riemann sums using the midpoint rule.
Do not evaluate it.

Attachment 25753

Please help
Thanks in advance
November 16th 2012, 04:36 PM
Plato

Re: Limit of Riemann sums

Quote:

Originally Posted by nubshat

Express the following integral as the limit of Riemann sums using the midpoint rule
Attachment 25753

You are asking us to do this for you. NO WAY!
Note that $f(x)=\frac{x^2}{x^6+1}$ is an even function.
So the question reduces to $2\int_0^1 {f(x)dx}$ .

To partition the interval $[0,1]$ into $n$ regular subdivision we get $\Delta_x=\frac{1}{n}$ .
Then $x_k=k\cdot\Delta_x,~k=0,~1,\cdots,~n$ .
The midpoints are $m_k=\frac{x_k-x_{k-1}}{2},~k=1.\cdots,n$ .
Now the midpoint sum is $\sum\limits_{k = 1}^n {f\left( {m_k } \right)\Delta _x }$
November 16th 2012, 05:33 PM
nubshat

1 Attachment(s)

Re: Limit of Riemann sums

Thank you very much for the help
I got Attachment 25755 as an answer
Can someone please confirm that this is right or tell me what I did wrong?
edit: the x is suppose to be an n

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