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 November 28th, 2013, 10:38 AM #1 Member   Joined: Oct 2012 Posts: 76 Thanks: 0 Riemann Integration Find $\int_{0}^{1}\: \sqrt{x}\: dx$ using a limit of Riemann sum.
 November 28th, 2013, 06:32 PM #2 Senior Member   Joined: Aug 2012 Posts: 2,323 Thanks: 715 Re: Riemann Integration Is this a homework problem or something you made up? When I set up the Riemann sum I ended up with an expression involving the sum of the square roots of the first n positive integers. There is a complicated formula for that involving Bernoulli numbers. So this is a hard problem unless there's some trick I didn't see.
November 28th, 2013, 11:22 PM   #3
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Re: Riemann Integration

Quote:
 Originally Posted by Maschke Is this a homework problem or something you made up? When I set up the Riemann sum I ended up with an expression involving the sum of the square roots of the first n positive integers. There is a complicated formula for that involving Bernoulli numbers. So this is a hard problem unless there's some trick I didn't see.
exactly, when you use a fractionation regular $x_{i}=\frac{i}{n}$ you will get a complicated formula. However, if you use not a regular fractionation as $x_{i}=\frac{i^2}{n^2}$ , you can deal with this.

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### Formula of sum squares of positive integers of Riemann integral

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