Question

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

y = 8x³,    y = 0,    x = 1;    about x = 2

Answer 1

Shell method Consider the region bounded by the curves y -8x',y 0,x-1. Need to find the volume of the solid obtained by rotating the given region about the line Use shell method The bounded region R and the shell is shown below 10 9.5 8.5 7.5 6.5 5.5 Shell radius 4Shell height 3.54 h(x)-8r 3 2.5 2 0.5 -0 0.5 2.5 3.5 4.5 Obtained solid is shown below:

Shell radius P(x) 2-x Shell height h(x) = 8x3 And x varies from 0 to 1 . The the volume is

= 167 20 1671- 24 24 Hence the required volume is