Science:Math Exam Resources/Courses/MATH103/April 2011/Question 03 (b)
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Question 03 (b) 

Consider the function . Find the total, finite area bounded by and the axis. 
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 

In your sketch from part (a), shade in the region(s) bounded by the graph of and the axis. 
Hint 2 

Write the area as an integral or sum of integrals. 
Hint 3 

Be careful to account for changes in the sign of 
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 area of the region bounded by the graph of and the  axis is
In the third line, we've expanded the factors of into the sum
