MATH101 April 2017
• Q1 (a) • Q1 (c) • Q1 (d) • Q2 (a) • Q2 (b) • Q2 (c) (i) • Q2 (c) (ii) • Q2 (c) (iii) • Q3 (a) • Q3 (b) • Q4 (a) • Q4 (b) • Q5 (a) • Q5 (b) • Q6 (a) • Q6 (b) • Q7 (a) • Q7 (b) • Q8 • Q9 • Q10 • Q11 (a) • Q11 (b) • Q11 (c) •
Question 03 (a)
Find the area of the region between the curves and . A calculator-ready answer is sufficient.
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!
Find the points of intersection of the two graphs to determine the integration limits for the area.
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Consider the two curves and . Note that is a line, and is a parabola whose leading coefficient is negative (so it is shaped like an up-side-down U).
First, we find the intersection points of the two graphs. By solving
the intersection points are obtained at and .
Then, the area we are looking for is
Either drawing the graphs or plugging a number in the interval , we can see that
Therefore, we have on and plug this into integral to have
Here, the Power Rule of differentiation is used. Therefore, the area between the two graphs is