Mathematics-I (3110014)

BE | Semester-1   Winter-2019 | 17-01-2020

Q3) (c)

Find the volume of the solid generated by rotating the plane region bounded by y=1x, x=1, x=3 about the X axis.

The cross-section AB of the generated volume, is a circle of radius y perpendicular to  X  axis. [ From Fig. 1 ]

Volume of solid is given by,

V=πx=ax=by2 dx

V=πx=1x=31x2 dx

V=πx=1x=3x-2 dx

V=πx-1-113

V=-π1x13

V=-π13-1

V=-π-23

V=2π3