Help with Riemann sums.

Ste234

I have a midterm on thursday and really can't do the Riemann sum questions, could someone perhaps go through this question with me?

eoins23456

How do you pronounce Riemann?

equivariant

eoins23456 wrote: »

How do you pronounce Riemann?

Ree-man

Michael Collins

The limit of the Riemann sum above is the definition of the Riemann integral. The xi's partition the x-axis into rectangles (I'm sure you've seen this picture), as n increases there are more and more rectangles and the sum becomes closer to the area under the curve.

As n -> infinity, the area becomes exact and you have the limit equal to the corresponding integral. You're asked to give this integral and evaluate it.

See if you can write down the integral first. All you need to do is identify the lower and upper limits (you can get this from the xi formula by subbing in the two extreme i values). The integrand should be obvious from the Riemann sum forumula.

Then you just need to evalutate this integral - but don't worry about that yet. Post back your integral when you have it!

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https://www.youtube.com/watch?v=gFpHHTxsDkI

This might be just what you're looking for.