MATH101 April 2017
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q2 (a) • Q2 (b) • Q2 (c) (i) • Q2 (c) (ii) • Q2 (c) (iii) • Q2 (c) (iv) • 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 02 (a)
Which integral represents the area to the right of the curve and to the
left of the curve ?
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!
View both curves as functions of ; i.e., express the equations of each of these curves in the form .
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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We consider the region between two curves and .
First, we find the intersection points. Since two curves can be written as and , plugging the first one into the second one, we get
Therefore, the intersection points are and .
On the other hand, according to the question, the curve lies on the right side of , so that when .
To summarize, the area between the two curves has to be an integral of the form
The last equality follows from the fact that is even. Therefore, the answer is .