Science:Math Exam Resources/Courses/MATH101/April 2017/Question 03 (a)
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Question 03 (a) 

Find the area of the region between the curves and . A calculatorready answer is sufficient. 
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 

Find the points of intersection of the two graphs to determine the integration limits for the area. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Consider the two curves and . Note that is a line, and is a parabola whose leading coefficient is negative (so it is shaped like an upsidedown U). First, we find the intersection points of the two graphs. By solving
the intersection points are obtained at and .
Then, the area we are looking for is .
Either drawing the graphs or plugging a number in the interval , we can see that when . Therefore, we have on and plug this into integral to have
Here, the Power Rule of differentiation is used. Therefore, the area between the two graphs is
Answer: 