5.1 Integration & Anti-derivatives Area Estimate Under a Function Question #5 (Medium)

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Published on 4 Feb 2013
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5.1 Integration & Anti-derivatives
Area Estimate Under a Function
Question #5 (Medium): Interpreting the Limit
Strategy
This is same as Question #4 but working backwards.
Based on the limit expression:  

1) Determine the interval from  
2) Convert  into a regular function notation  without the subscript .
Sample Question
Find the functional region whose area is equal to the limit.


  

Solution
1) It looks like  
, and since   ,  
fits the form of . So must be .
2)   
and since   , then  


, which means   so   .
So the interval is , ie.     
3) Since  
  , then  
Therefore, the limit 

  
 represents the area under the function  over the
interval  (ie.     .