My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
November 22nd, 2014, 03:58 PM   #1
Member
 
Joined: Sep 2014
From: Cambridge

Posts: 64
Thanks: 4

Riemann Sums (check my work)

Hi, did I solve this correctly?
Attached Images
File Type: jpg 11111.jpg (100.9 KB, 9 views)
File Type: jpg 20141122_195242.jpg (90.2 KB, 8 views)
Omnipotent is offline  
 
November 23rd, 2014, 02:34 AM   #2
szz
Senior Member
 
szz's Avatar
 
Joined: Oct 2014
From: EU

Posts: 224
Thanks: 26

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
File Type: jpg tmp.jpg (19.3 KB, 15 views)
File Type: jpg tmp2.jpg (17.5 KB, 15 views)
File Type: jpg tmp0.jpg (21.2 KB, 15 views)

Last edited by szz; November 23rd, 2014 at 03:28 AM.
szz is offline  
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.
Omnipotent is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
check, riemann, sums, work



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Riemann Sums slabbxo Calculus 1 February 25th, 2014 04:52 AM
Riemann Sums... n3rdwannab3 Calculus 1 January 17th, 2014 03:41 PM
Help please on Riemann sums mctiger Real Analysis 0 May 5th, 2013 07:03 AM
Limit of Riemann sums nubshat Calculus 1 November 17th, 2012 07:55 AM
Riemann sums nubshat Calculus 2 November 13th, 2012 05:04 PM





Copyright © 2019 My Math Forum. All rights reserved.