http://www.ck12.org Chapter 5. Applications of Definite Integrals

Figure 11b
From the formula above,

V(x) =

∫b

a π

([f(x)] (^2) −[g(x)] 2 )dx

∫ 3
0 π
((x (^2) + 1 ) (^2) −(x) 2 )dx

∫ 3
0 π
(x (^4) +x (^2) + 1 )dx
=^3035 π.
The methods of disks and washers can also be used if the region is revolved about they−axis. The analogous
formulas can be easily deduced from the above formulas or from the volumes of solids generated.
Disks:

V=

∫d

c π[u(y)]

(^2) dy.
Washers:

V=

∫d

c π

([w(y)] (^2) −[v(y)] 2 )dy.
Example 5: