Science:Math Exam Resources/Courses/MATH103/April 2016/Question 02 (d)
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Question 02 (d) 

Compute the following integral:

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 

Write and consider integrating by parts. 
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Solution 1 

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Please rate my easiness! It's quick and helps everyone guide their studies. We first write and use integration by parts. Thus let and We then have and Applying integration by parts then gives In order to evaluate the resulting integral, we use the substitution obtaining Hence 
Solution 2 

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Please rate my easiness! It's quick and helps everyone guide their studies. We can use the formula for antiderivatives of the inverse of a (continuous, invertible) function ; namely, where is an antiderivative of .
By the Pythagorean identity, we know that so which yields the final answer of 