Science:Math Exam Resources/Courses/MATH101 A/April 2024/Question 02
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Question 02 |
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Find the area of the region under the curve and above the -axis. |
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 |
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It may be helpful to first visualize the curve by plotting and identifying where it intersects the axis. Next, you can think about what mathematical tools we can use to find the area under the curve between these points. |
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.
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Solution |
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First, we identify the points where the curve intersects the axis by solving which yields . Thus, the region of interest lies above the x-axis on the interval . This is represented as the shaded region in the attached graph. To determine the enclosed area, we set up a definite integral to compute the area under the curve from to :
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