Science:Math Exam Resources/Courses/MATH105/April 2012/Question 08 (f)
• Q1 (a) • Q1 (b) • Q1 (c) • Q2 (a) • Q2 (b) • Q2 (c) • Q3 (a) • Q3 (b) • Q4 (a) • Q4 (b) • Q5 (a) • Q5 (b) • Q6 (a) • Q6 (b) • Q7 (a) • Q7 (b) • Q8 (a) • Q8 (b) • Q8 (c) • Q8 (d) • Q8 (e) • Q8 (f) • Q8 (g) • Q8 (h) • Q8 (i) •
Question 08 (f) 

Shortanswer questions. No credit will be given for the answer (even if it is correct) without the accompanying work. Find a bound for the error in approximating using Simpson’s rule with n = 6 subintervals. There is no need to simplify your answer. Do not write down the Simpson’s rule approximation S_{n}. 
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 

Recall that if on the interval , then the error in using to approximate has absolute value less than or equal to . 
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 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. The error bound for Simpson's rule requires us to find the fourth derivative of the integrand. For , we find: and To find our K, we need to know the largest can be over the integration range . is a decreasing function, with its largest value on being at , so K = 16. The error with is bounded by . Note: the question did not ask us to evaluate the Simpson's rule approximation; we were only asked to bound its error. 