Science:Math Exam Resources/Courses/MATH103/April 2016/Question 03
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Question 03 

Find the length of the curve from to . 
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 

Recall the arc length formula (see the next hint if you need a reminder). 
Hint 2 

The arc length of the curve defined by the graph of is 
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. By the arc length formula, the length of the curve defined by the graph of from to is given by So for the curve from to we have Using the substitution the length can be computed as 