MATH200 December 2013
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Question 05 (a)
This question is about the integral
(a) Sketch the domain of integration
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!
The bounds of integration tell us that
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We have to start by drawing the following curves to see the domain of integration
and are just horizontal lines at and respectively (shown below).
represents a line
represents half a circle of radius defined for . In our case, only the part of the half circle in the first quadrant is necessary because of and .
As a result, the domain of integration is the area bounded by these four curves.