
Applications of Integration 15-41
= +
=
p
p
128
5
34
5
162
.
Example 15.34 Find the area of surface generated by rotating the region bounded by the curves
y = x
3
- 6x
2
+ 11x - 6 and x axis around y axis.
Solution: Since the axis of revolution of y-axis we use cylindrical shell method to find the volume.
The points of intersection of curves are x = 1, 2, 3.
By the cylindrical shell method, the volume of the solid of revolution generated by y = f(x) by revolving
around y axis between the lines x = a and x = b is given by,
V xf x dx x x x x dx
x x x x dx
a
b
=
∫
= − + −
∫
= − + −
2 2 6 11 6
2 6 11 6
3 2
1
3
4 3 2
p p
p
( ) ( )
( )
11
3
5 4 3 2
1
3
5 4 3