Science:Math Exam Resources/Courses/MATH101/April 2012/Question 03 (b)
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Question 03 (b) 

Evaluate 
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 

Try to write the integral as a sum of two integrals that you can calculate. 
Hint 2 

The integral can be interpreted geometrically. 
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. We can write the integral as . Now we compute: for we use the substitution to get: For we note that this corresponds to one fourth of the area of a circle of radius 3, so Hence the final result is 