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mt166s2010_2

# mt166s2010_2 - y = cos x and the x-axis between x =-π 2...

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Math 166 Midterm Exam Part II February 25, 2010 Full Name: Instructor & Section: Instructions: Answer each question as completely as you can. Show all work, including the steps in your calculations. Full credit will not be given for answers without supporting work. Give exact values in your results. 1. (15 points) Sketch the region R bounded by the graph of y = 4 - x 2 , the y -axis, and the horizontal line y = 1, and then find the area of R . A solid is generated by revolving the region R about the x -axis. Set up, but do not evaluate , definite integrals for the volume of the resulting solid of revolution using the method of: (a) Washers; (b) Cylindrical Shells.

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Math 166 Midterm Part II Page 2 2. (15 points) Find the centroid of the region bounded by the graph of

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Unformatted text preview: y = cos x and the x-axis, between x =-π/ 2 and x = π/ 2. Make a sketch and use symmetry where possible. Math 166 Midterm Part II Page 3 3. (10 points) The corn in a grain silo, which has the shape of a right circular cylinder, is to be lifted out over the top edge of the silo. The silo is 20 feet in diameter and is 30 feet high. If the corn in the silo has a uniform depth of 25 feet, how much work is done in lifting all of the corn out of the silo? [Use δ lb / ft 3 for the (weight) density of the corn.] Math 166 Midterm Part II Page 4 4. (10 points) Find the length of the parametric curve x = 3 t 2 , y = 2 t 3 , 0 ≤ t ≤ 2....
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mt166s2010_2 - y = cos x and the x-axis between x =-π 2...

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