Science:Math Exam Resources/Courses/MATH101/April 2017/Question 04 (a)
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Question 04 (a) 

Let be the region above the curve and below the line . The area of the region is (you do not have to prove that). Find the centroid of the region . Simplify your answer completely. 
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 

Use the formulas for the centroid
with the appropriate choice of . 
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.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The points of intersection are given by , which implies . Using the formulas for the centroid:
and replacing , we have
Answer: 