Find the Riemman Sum of the integration of x^3 from 1 to 2.

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- July 19th 2006, 11:31 AMNimmyCalculus I Help?
Find the Riemman Sum of the integration of x^3 from 1 to 2.

- July 19th 2006, 12:23 PMThePerfectHackerQuote:

Originally Posted by**Nimmy**

I will partition the region with right-endpoint.

Take interval divide it in equal regions. Thus, each one has length .

Thus, the Riemann sum is,

Rewrite is as,

Thus,

Which simplifies to,

Do you also want to know its value? - July 19th 2006, 12:33 PMgalactus
Do you mean the tedious technical approach?.

Using right endpoint.

Expanding and summing:

Now, remember the 'identities':

Now, use those and it all whittles down to:

Perform the 'easy' integration and see if you get the same thing.