MA 16200 Study Guide - Final Guide: Partial Fraction Decomposition, Trigonometric Substitution
30 Apr 2016
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The area of the region enclosed by the curves and is given by: Plug in: the volume of the solid obtained by rotating about the x-axis the region in the first quadrant bounded by the graphs of , , and is given by: Let be the region bounded by the curves and. Using the method of cylindrical shells, the volume of the solid generated by rotating about the x-axis is given by: When x = 0, y = 0 and when x = 2, y = 4. Plug in: a right circular conical tank of height 20 ft. and base radius ft. has its vertex and the bottom (the origin), and its axis vertical (the y-axis). If the tank is full of water at 62. 5 lb. /cu. ft. , the work required to pump all the water over the top is: Find the work done moving a thin layer all the way to the top (width will be dy, height is y)
