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

Printable View

- Nov 16th 2012, 02:30 PMnubshatLimit 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 - Nov 16th 2012, 04:36 PMPlatoRe: Limit of Riemann sums
You are asking us to do this for you. NO WAY!

Note that $\displaystyle f(x)=\frac{x^2}{x^6+1}$ is an even function.

So the question reduces to $\displaystyle 2\int_0^1 {f(x)dx} $.

To partition the interval $\displaystyle [0,1]$ into $\displaystyle n$ regular subdivision we get $\displaystyle \Delta_x=\frac{1}{n}$.

Then $\displaystyle x_k=k\cdot\Delta_x,~k=0,~1,\cdots,~n$.

The midpoints are $\displaystyle m_k=\frac{x_k-x_{k-1}}{2},~k=1.\cdots,n$.

Now the midpoint sum is $\displaystyle \sum\limits_{k = 1}^n {f\left( {m_k } \right)\Delta _x } $ - Nov 16th 2012, 05:33 PMnubshatRe: 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