Question to Find Volume of a Solid Using Graphical Representation

Topic : Volume of a Solid

Question :Use the disk or the shell method to find the volume of the solid generated by revolving the
region bounded by the graphs of the equations about each given line.
y = 10/x^2 , y = 0 , x = 1 , x = 5
a. the x-axis
b. the y-axis
c. the line x=4

Solution :

The graph of the curve y = 10/ x^2 between the two axes and the lines x = 1 and x = 5 is
denoted by the shaded region in the graph drawn below:

(a.) the x-axis
We know that the volume of the solid formed by rotating the area between the curve of f(x) and
the lines x = a and x = b about the x-axis is given by

(b.) y-axis
We know that the volume of the solid formed by rotating the area between the curve of f(x)
and the lines x = a and x = b about the y-axis is given by

(c.) x=4
When the shaded region is revolved about the line x = 4, then the distance from the axis of
rotation is reduced from 4(the horizontal distance is the difference of the x-coordinates)
So, the curve reduces to