MATH103 April 2005
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q2 • Q3 (a) • Q3 (b) • Q3 (c) • Q4 • Q5 (a) • Q5 (b) • Q5 (c) • Q6 (a) • Q6 (b) • Q6 (c) • Q7 (a) • Q7 (b) • Q7 (c) • Q8 (a) • Q8 (b) • Q8 (c) •
Question 01 (c)
Multiple Choice Question: Select ONE correct answer (i), (ii), (iii), (iv), or (v).
(c) An approximation to the integral
using n rectangles would be
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint.
This is a Riemann sum question.
Use the relationship between the Riemann sum of a function and its integral. This is given by
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The Riemann Sum approximation is
where n represents the total number of rectangles, k enumerates the particular rectangles, and will be equal to
In this case, and
Therefore, the solution is (v).
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