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# w06 - Math 152 Workshop 6 Spring 2011 1 The region R is...

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Math 152 Workshop 6 Spring 2011 1. The region R is bounded below by the x -axis, bounded on the left by the line x = 1, bounded on the right by the line x = 2, and bounded above by the curve y = 5 + x x 2 + 4 x + 3 . (a) Sketch the region R and set up a definite integral that gives the area of R . Then calculate the integral in two ways: i. Approximately using the fnInt( program in your calculator. ii. Exactly using the method of partial fractions. iii. Check that the two answers are “the same” (that is, find approximate values for the result of the second method). (b) The region R is rotated around the x -axis to generate a solid body B . Sketch B and set up a definite integral that gives the volume of B . Calculate the integral in two ways: i. Approximately using the fnInt( program in your calculator. ii. Exactly using the method of partial fractions (be careful how you set this up – there are four undetermined coefficients in the partial fraction decomposition).
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