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 Calculus Calculus Math Forum

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

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Riemann Sums (check my work)

Hi, did I solve this correctly?
Attached Images 11111.jpg (100.9 KB, 9 views) 20141122_195242.jpg (90.2 KB, 8 views) 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
Attached Images tmp.jpg (19.3 KB, 15 views) tmp2.jpg (17.5 KB, 15 views) tmp0.jpg (21.2 KB, 15 views)

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. Tags check, riemann, sums, work Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post slabbxo Calculus 1 February 25th, 2014 04:52 AM n3rdwannab3 Calculus 1 January 17th, 2014 03:41 PM mctiger Real Analysis 0 May 5th, 2013 07:03 AM nubshat Calculus 1 November 17th, 2012 07:55 AM nubshat Calculus 2 November 13th, 2012 05:04 PM

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