MATH101 April 2006
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Question 02 (a)
Full-Solution Problems. Justify your answers and show all your work. Simplification of answers is not required.
Sketch the bounded region that lies between the curves and , and show that the area of this region equals .
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 - then draw the picture.
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A picture is included below.
First, find the points of intersection.
Take the positive values of first and solving gives
and so is a solution here (notice that we discard since we started with only the positive x values first). Now, taking the negative x values gives
and so is the other solution. Now, we can draw the picture (see below). The picture clearly shows that the upper function is 2-x2, and that the function is an even function. So we see that it suffices to compute
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