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# C4 Question on Vectors ! watch

1. Hello, pls can someone explain this question to me ! Question 9 iv) I don't really understand why they have decided to involve the rectangle into it? I thought that the area of the shaded portion was simply ln(3/2) , because they are simply reflections right? Where did the rectangle come if from suddenly? Any help would be greatly appreciated! Thanks!

http://www.mei.org.uk/files/papers/2012_Jan_c3.pdf
2. The rectangle that they refer to is shown here in red.

3. Firstly, this is an integration question from C3, not a vector question from C4!

For 9(iv) the ln(3/2) that you have worked out corresponds to the the white area in the red rectangle shown above. Since g(x) and f(x) are the inverse of each other, if you rotate the red rectangle by 90 degrees clockwise you will see another rectangle, if you will. As the area of the rectangle is 2*ln(4/3) (you should have worked this out in the previous parts of the question), then the area of the shaded region (worked out by subtracting the area of the white region from the rectangle) is simply:

2*ln(4/3) - ln(3/2)
=ln(16/9) - ln(3/2)
=ln(32/27).

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Updated: April 10, 2013
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