MATH101 April 2012
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q1 (g) • Q1 (h) • Q1 (i) • Q1 (j) • Q2 (a) • Q2 (b) • Q3 (a) • Q3 (b) • Q3 (c) • Q3 (d) • Q4 (a) • Q4 (c) • Q5 • Q6 • Q7 (a) • Q7 (b) • Q7 (c) • Q8 (a) • Q8 (b) •
Question 02 (a)
Let R be the bounded region that lies between the curve and the line . Sketch R and find its area.
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!
Where does the two curves intersect?
If you find the values of x, namely a and b (where a<b) so that the curves intersect, then the area bounded by the two curves is given by
where f(x) denotes the curve above the region R and g(x) denotes the curve below respectively.
You will need the sketch to determine which curve is above and which is below.
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Since the two curves and intersects when
Thus, the curves intersect at x=-1 and x=2. Moreover, from the sketch, we can see that f(x) > g(x) in the interval [-1, 2].
Therefore, the area A bounded by the curves is given by:
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