MATH101 April 2010
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q2 (a) • Q2 (b) • Q2 (c) • Q3 (a) • Q3 (b) • Q3 (c) • Q3 (d) • Q4 • Q5 (a) • Q5 (b) • Q5 (c) • Q6 • Q7 • Q8 • Q9 •
Evaluate by computing the limit of the right-endpoint Riemann sums as .
You may use the formula .
No credit will be given for computing this integral using antidifferentiation, although you may use antidifferentiation to check your answer.
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!
The right Riemann sum for the function is:
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.
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The interval has size 1 so . The interval is so . In this case so the right Riemann sum is:
So the integral is:
Checking our answer, we see that
which matches the above.
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