Science:Math Exam Resources/Courses/MATH105/April 2013/Question 01 (g)
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Question 01 (g) 

ShortAnswer Questions. Put your answer in the box provided but show your work also. Each question is worth 3 marks, but not all questions are of equal difficulty. Find the area of the region bounded by the graph of and the axis between and . 
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 

The area between a curve and the xaxis is just the integral from the function on the region. 
Hint 2 

Use the substitution u = 2x4. 
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 proceed directly using the hints. First, the area is given by Using the substitution u = 2x4 we find du = 2dx. When x = 0 we find u = 4, when x = 1 we find u = 2. Hence 