Science:Math Exam Resources/Courses/MATH105/April 2016/Question 01 (l)
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Question 01 (l) 

Let be the region bounded by the graph of and the axis on the interval , where is a constant. Find the value of such that the area of the region is 1. 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Write the area in terms of an integral in the interval 
Hint 2 

You are dealing with an improper integral. 
Checking a solution serves two purposes: helping you if, after having used all the hints, 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 region bounded by the function and xaxis from is We first note that this is an improper integral, and we need to rewrite it as the following:
We now apply the substitution to simplify the integral. Note that and since is changing between and then is changing between and . Therefore, = We know that the area of the region is 1. This implies that
We finally get
