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HH_Sec_8_1

# HH_Sec_8_1 - 1 60 π cubic meters x 1 y(meters 1 y = x 1 3...

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(9/30/08) Math 10B. Lecture Examples. Section 8.1. Areas and volumes Example 1 The base of a solid is the region between the curves y = 1 2 x 2 and y = 1 - 1 2 x 2 for 0 x 1 in an xy -plane and its cross sections perpendicular to the x -axis are squares. Find its volume. Answer: Figures A1a and A1b [Volume] = 8 15 x 1 y 1 x y = 1 2 x 2 y = 1 - 1 2 x 2 1 x y x Base of the solid The solid Figure A1a Figure A1b Example 2 The intersection of a solid with an xy -plane with distances measured in meters is the region R between the curves y = x 1 / 3 and y = 4 3 x 1 / 3 for 0 x 1 . The cross sections of the solid perpendicular to the x -axis are circles with diameters in the xy -plane. Find its volume. Answer: Figures A2a and A2b. [Volume] =
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Unformatted text preview: 1 60 π cubic meters x 1 y (meters) 1 y = x 1 / 3 y = 4 3 x 1 / 3 x (meters) R [Radius] = 1 6 x 1 / 3 The region The cross section at x Figure A2a Figure A2b Interactive Examples Work the following Interactive Examples on Shenk’s web page, http//www.math.ucsd.edu/˜ashenk/: ‡ Section 7.3: Examples 1 and 2 † Lecture notes to accompany Section 8.1 of Calculus by Hughes-Hallett et al ‡ The chapter and section numbers on Shenk’s web site refer to his calculus manuscript and not to the chapters and sections of the textbook for the course. 1...
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