November 21st, 2017, 05:36 PM  #1 
Newbie Joined: Apr 2016 From: Wonderland Posts: 23 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, 06:21 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,671 Thanks: 2651 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 ($x$). 

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converting, integral, limits 
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