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Math1210 Weekly Assignment 11 Spring, 2016 (Areas and volumes 5.1) instructor: Uid number: name: Instructions: Please show all of your work as partial credit will be given where appropriate, and there may be no credit given for problems where there is no work shown. All answers should be completely simplified, unless otherwise stated. No calculators or electronics of any kind are allowed. (Total of 50 points possible.) 1. (20 points) Sketch the regions bounded by the graphs of the following functions and then compute their areas using integrals, after figuring out which slicing is the most appropriate (vertical or horizontal). (a) y = x2 − 4x − 5, 2 (b) x = 8y − y , 2 y=0 x=0 (c) y = x − 2x, y = −x2 (d) x = y 2 − 2y, x−y−4=0 Page 2 2. (10 points) Find the area of the triangle with vertices at (−1, 4), (2, −2) and (5, 1) using integration. Page 3 3. (10 points) Find the formula for the volume of a cone of base radius r and height h using the appropriate integration method from Section 5.2. Page 4 4. (10 points) Find the volume of the solid generated by revolving around the x-axis the region bounded by the line y = 6x and the parabola y = 6x2 . Page 5