Science:Math Exam Resources/Courses/MATH101/April 2009/Question 01 (e)
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Question 01 (e) 

Find the length of the curve 
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 

For this problem, the look of the problem should tell you that you should try to think about the arc length formula but with the roles of x and y switched. That is, think of x as a function of y (instead of the usual thinking of y as a function of x). 
Hint 2 

In the setting of the first hint, the length of this curve is equal to
for some values of and . 
Hint 3 

A final substitution should take you to an easy to evaluate integral and thus the final answer. 
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 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. To solve this question, the question itself hints that we should be thinking as x as a function of y. Now,
Let so that . Changing the endpoints gives and . Thus,
