My Math Forum Riemann Sums (check my work)

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November 22nd, 2014, 03:58 PM   #1
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From: Cambridge

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Riemann Sums (check my work)

Hi, did I solve this correctly?
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November 23rd, 2014, 02:34 AM   #2
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Math Focus: Calculus
Hi Omnipotent,

I don't understand how and why you have to divide the area by 4 pieces as such.
Maybe the 4 region are the given by the intersections between $\displaystyle x = 0$ and $\displaystyle x = 15$.

However, if I should have to determine the area of the triangle you chose with Riemann Integration, I would start expressing the function as a piecewise function:

$\displaystyle f(x) = \left\{\begin{matrix} |\, 2x \,| & \text{if} & x < 5\\ |\,-x + 15 \,| & \text{if} & x \geq 5 \end{matrix}\right.$

Once that, I would calculate:

$\displaystyle \int_0^{15} f(x)\,\text{d}x = \int_0^5 | 2x | \,\text{d}x + \int_5^{15} | -x+15 | \,\text{d}x$

which is:

However, if the 4 regions are given by the intersections of the function, I think (which does not mean I am right) that the lower sum is given by the area of the smallest triangle:

In this case the area is given by the Riemann Integral:

$\displaystyle \int_0^5 -x+15\,\text{d}x- \int_0^5 2x\,\text{d}x$

Cheers
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Last edited by szz; November 23rd, 2014 at 03:28 AM.

 November 24th, 2014, 09:21 AM #3 Member   Joined: Sep 2014 From: Cambridge Posts: 64 Thanks: 4 Thank you, however I forgot to add that our professor told us not to use calculus for this problem. He does this thing where first you figure it out the hard way and then u see the trends and then understand the concept.

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