Riemann Sums and Integrals

**Billy Maize** · August 29th 2009, 08:35 AM

Question: Find the integral of the equation 2x+1 from 0 to 3 using Riemann Sums.

Please show me how to do this, I keep on getting 9 as the answer, but it is actually 12.

**eXist** · August 29th 2009, 08:52 AM

It depends on the Riemann Sum that you use. Either right, left or center. Also it depends on how many intervals you split it up into. Are there anymore instructions to the problem?

**Billy Maize** · August 29th 2009, 08:55 AM

I am using right Reimann sums and I am using infinite intervals n->∞.

**eXist** · August 29th 2009, 09:01 AM

Then that's the same as the actual integral if $n \Rightarrow \infty$ . Cause that means that $dx \Rightarrow 0$ .

So, take the actuall integral and you get:

$\int_0^3 2x + 1\, dx = x^2 + x$ between 0 and 3.

$= 3^2 + 3 - (0^2 + 0)$

**Billy Maize** · August 29th 2009, 09:04 AM

ok thnks!

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