Science:Math Exam Resources/Courses/MATH101/April 2009/Question 03 (a)
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Question 03 (a) 

Let be the finite region in the plane bounded by , and . 
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! 
Hint 

The coordinates of the centroid are computed using the formulas and where 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The first point with where crosses the xaxis is at . Hence we have that and . Thus, we have
The xcoordinate of the centroid are computed using the formulas
To solve this, we use integration by parts. Let
Then,
Lastly, for the other coordinate, we have
Now we use the double angle formula
to see that
and so the centroid is
completing the proof. 