MATH105 April 2010
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q1 (g) • Q1 (h) • Q1 (i) • Q1 (j) • Q1 (k) • Q1 (l) • Q1 (m) • Q1 (n) • Q2 • Q3 • Q4 • Q5 (a) • Q5 (b) • Q5 (c) • Q6 •
Question 01 (e)
Compute the average value of
over the interval 1 ≤ x ≤ e.
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!
What is the definition for the average value of a function, , on an interval, ?
See the related wikipedia article. Note that mean and average have the same meaning in this context.
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This is simple matter of evaluating an integral. From the definition of the average value of a function on an interval, we can write an expression for the average value of on the interval :
So the average value of on the interval is .
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