Science:Math Exam Resources/Courses/MATH101/April 2010/Question 05 (b)
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Question 05 (b) 

FullSolution Problem. Justify your answer and show all your work. Simplification of the answer is not required. An unknown function has the following values: , , , , Write down the Simpson's approximation for 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

The formula for the Simpson's rule is given by
where as always is an even integer. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The formula for the Simpson's rule is given by When , we have that and thus, the Simpson's rule approximation that we need is 