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Lecture

MAT136H1 Lecture Notes - Trapezoidal Rule


Department
Mathematics
Course Code
MAT136H1
Professor
all

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7.7 Integral Techniques
Integral Approximation
Question #2 (Medium): Approximating the Integral
Strategy
Recall the approximate expressions for the five methods covered in the unit. Notice that  
no
matter which approximating method is used.
Sample Question
Approximate the integral (answers rounded to 6 decimal places) with the specified value of using:
1) Midpoint Rule
2) Trapezoidal Rule
3) Simpson’s Rule

,   
Solution
Given    and interval of , then  

.
1) Midpoint Rule:
 
 
  
 
The intervals are: 
,
, 
,
, 
,
. Corresponding midpoints for each
interval are:

, where the distance in between are  
. Then for example,
  . Therefore,
   
 
 
2) Trapezoidal Rule:
     

       
 
3) Simpson’s Rule: 
      
        


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