MATH101 April 2008
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q1 (g) • Q2 (a) • Q2 (b) • Q2 (c) • Q2 (d) • Q3 (a) • Q3 (b) • Q3 (c) • Q3 (d) • Q4 (a) • Q4 (b) • Q5 (a) • Q5 (b) • Q6 • Q7 (a) • Q7 (b) •
Question 01 (c)
as a definite integral. Do not evaluate the integral.
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!
This is a Riemann sum. Recall that
Then do a pattern match.
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From the question, we immediately see that
Now, to determine , notice that we have that the function is of the form
The only composition of functions is underneath the square sign. So we must have that
and hence that
As , we have that and hence since
we have that . Combining the above gives
which completes the question.
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MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Riemann sum