M2D1 Math 242.docx - Castaneda Andrew I 18 Aug 2020...

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Castaneda, Andrew I 18 Aug 2020 Calculus 2 Professor Ayanaw Hagos Math 242 (Calculus 2) Module 2 Discussion 1 PROBLEM: 1) Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by x=−3y2+12y9,x=0about the x-axis. GOALS: Use the cylindrical shell method to find the volume of a solid SETUP: 1) Graph the function x =− 3 y 2 + 12 y 9 . We get: 2) Since we are using cylindrical shells, we can place a rectangle that starts at x=0 and goes to the bounds of the curve 3) The thickness of the rectangle is in terms of ‘y’, so all the components of our integral will have to be in terms of ‘y’.

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