5.4. Area of a Surface of Revolution http://www.ck12.org
Figure 21
The surface areaSis
S=
∫b
a^2 πy√
1 +
(dy
dx) 2
dx=∫ 2
0 2 πx3 √ 1 +( 3 x (^2) ) (^2) dx
= 2 π
∫ 2
0 x
(^3) ( 1 + 9 x (^4) ) 1 / (^2) dx.
Usingu−substitution by lettingu= 1 + 9 x^4 ,