Science:Math Exam Resources/Courses/MATH101/April 2005/Question 02 (a)
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q1 (g) • Q2 (a) • Q2 (b) • Q2 (c) • Q2 (d) • Q3 (a) • Q3 (b) • Q3 (c) • Q4 • Q5 (a) • Q5 (b) • Q6 (a) • Q6 (b) • Q7 (a) • Q7 (b) • Q7 (c) • Q8 (a) • Q8 (b) •
Question 02 (a) 

FullSolution Problem. Justify your answer and show all your work. Simplification of your answer is not required. Let be the finite region bounded above by the curve and bounded below by
Carefully sketch and find its area explicitly. 
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 

There are two key things to figure out. One is the points of intersection and the other is which curve is larger on the region of integration. 
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 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. A picture can be found below. First, we find the points of intersection. Set the curves equal to each other so that
Then isolating to one side gives
and so the x coordinates of the points of intersection are . Now, plugging in the point into both curves shows that is the upper most curve. Hence, the area we seek is
completing the question. 