Question

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. 1 y = 8x + y = 0 X=0 X = 9

Answer 1

1 1 y= y = 8x+7 V8x +7 x=0 X-axis x=9 y=0 x-axis 3-D Shape Graph 1 Here we will use washer method. Now the elementary area A(x) = 4( y?upper – y lower) - Cher -02 8x +7 1 => A(x) = ax 8.x +7 9 Then by washer method the volume of the give region revolving around x axis is = A(x) dx . x=0

1 In x + 20v |_ 40)d=/4473-*- --[-(2+3) --(_))--[-(7:2)--())":[~ * )--(3)] 77 = [ln (79) – In (8) – In (7) +In(8)] =- (In (79) – In (7)). 8 T Then the required volume is = (In (79) – In(7)). 8