Page 232 - Calculus Demystified

Applications of the Integral
CHAPTER 8

Fig. 8.4 219

As the mesh of the partition becomes finer and finer, this (Riemann) sum will tend
to the integral

b
A(x) dx.
a
We declare the value of this integral to be the volume V of the solid object.

8.1.2 EXAMPLES

EXAMPLE 8.1
Calculate the volume of the right circular cone with base a disc of radius 3
and height 6.

SOLUTION
ExamineFig.8.5.Wehavelaidtheconeonitsside,sothatitextendsfrom x =
0to x = 6. The upper edge of the figure is the line y = 3 − x/2. At position x,

y

3

6
x

Fig. 8.5