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Math 241 Homework 12 Solutions

Math 241 Homework 12 SolutionsSection solid lies between planes perpendicular to thex-axis atx=0andx=4. Thecross-sections perpendicular to the axis on the interval0 x 4are squares whose diagonals runfrom the parabolay= xto the parabolay= xSolution From the picture we haves2+s2=(2 x)2 2s2=4x s2=2xSince the area of the square is given byA=s2=2xwe haveVolume=S402x dx=x2U40=161 Problem solid lies between planes perpendicular to thex-axis atx= 1andx=1. Thecross-sections perpendicular to thex-axis are circular disks whose diameters run from the parabolay=x2to the parabolay=2 We haveDiameter=2 2x2 Radius=1 x2 Since the area of a circle is given by r2we haveVolume=S1 1( 2 x2+ x4)dx= x 2 x33+ x55 RRRRRRRRRRR1 1= 2 3+ 5

From the picture we have s2 +s2 =(2 ... squares whose bases run from the curve y = tan x to the curve y = sec x. 7. The base of a solid is the region bounded by the graphs of y = 3x, y = 6, and x = 0. The cross-sections perpendicular to the x-axis are a. rectangles of height 10.

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