November 21st, 2017, 06:36 PM  #1 
Newbie Joined: Apr 2016 From: Wonderland Posts: 20 Thanks: 0  Converting limits to integral
Hi all, I am lost trying to solve this limits question (see photo). Is there anything wrong with my method? I'm not very sure if I got the conversion right... https://imgur.com/a/2JnDw 
November 21st, 2017, 07:21 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,599 Thanks: 2587 Math Focus: Mainly analysis and algebra 
Think about the ordinals and the width of the strips. The ordinals here come at $\left(\frac{2i}{n}\right)$ for $i=0,1,\ldots,(n1)$. Thus the first ordinal is zero and the last is $\frac{2(n1)}{n}$. The strip width is $\frac2n$, so the right hand edge of the last ordinal is at $$\frac{2(n1)}{n}+\frac{2}{n} = 2$$ Thus your integral limits are at 0 and 2 and you just have to replace $\left(\frac{2i}{n}\right)$ with your variable of integration ($x$). 

Tags 
converting, integral, limits 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Solving limits with ln integral  liegex  Calculus  2  September 24th, 2017 02:44 PM 
Solve double integral by converting to polar coordinates  DakshD  Calculus  1  November 8th, 2016 12:38 PM 
Derivative of Integral With Limits  johnboy1985  Calculus  3  March 19th, 2015 05:47 AM 
converting Definite integral to indefine one  chessmath2009  Calculus  1  November 1st, 2012 04:35 AM 
Notation of integral limits  kunisch  Calculus  2  June 15th, 2010 11:37 AM 