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2006_solutions - Name April 2006 Marks[33 1 Short-Answer...

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Name: April 2006 Mathematics 101 Page 2 of 11 pages Marks [33] 1. Short-Answer 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. Full marks will be given for a correct answer placed in the box, but at most one mark will be given for an incorrect answer. Unless otherwise stated, simplify your answer as much as possible. (a) Find the average value of cos x on the interval [0 , π ]. Answer (b) Evaluate cos 2 x dx . Answer (c) Evaluate   1 1 x 2 + 1 x 2 dx . Answer Continued on page 3
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Name: April 2006 Mathematics 101 Page 3 of 11 pages (d) Write down the Simpson’s Rule approximation S 6 for 8 2 1 x 2 dx . You may leave your answer expressed as a sum of fractions. Answer (e) Calculate the volume of the solid obtained by rotating the region above the x -axis, below the curve y = x + x 2 , and between the lines x = 1 and x = 2 about the x -axis.
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