MATH105 April 2010
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q1 (g) • Q1 (h) • Q1 (i) • Q1 (j) • Q1 (k) • Q1 (l) • Q1 (m) • Q1 (n) • Q2 • Q3 • Q4 • Q5 (a) • Q5 (b) • Q5 (c) • Q6 •
Find the area of the region bounded by
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?
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What does this region look like? How can you find the area of such a region?
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First, we sketch each of the three curves to see what is the region that we are talking about.
We will need to find the coordinates of points A and B which are the intersection of curves. For A we have
We can see from the picture that we are interested in the point with a positive x coordinate, so
For B we have
And so since y = -2/x we have
This allows us to write the desired area as the sum of 2 integrals
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