202 PRACTICAL MATHEMATICS 



rk 



For the area B, V oy = TT x 2 dy 

 h 



-, 



Ja 



ncx n+1 dx, since dy = ncx"' 1 dx 

 Ttnc 



n+2 



- ffr+a _ a n+2) 



n+2 



( f k 



For the area A, V OY = TT { b 2 k a 2 h I x 2 



*. h 



+ l ^- - a + 2 l - -2 



n + 



For the area B, V ox = TT /A; 2 6 - ^ 2 a - |V dx\ 



(. Ja J 



c 2 a 8B + 1 -- - (b* n+l - a 2n+l )\ 

 2w+l v ; J 



Fig. 48 shows these four different surfaces of revolution. 



114. Example 1. In the curve y = 5x 2 , taking A as the area 

 bounded by the ordinates at x = 1 and x = 2, and B as the area 

 bounded by the abscissae corresponding to the ordinates at x = 1 

 and x = 2, find the volumes of the surfaces of revolution : 



(1) when the area A rotates about the axes of x and y respec- 



tively ; 



(2) when the area B rotates about the axes of x and y respec- 



tively. 



For the area A, V ox = TT I y z dx 



25:r I a? 4 cte 



li 



12 



M; 



= 57c{2 5 -l} 



= 486-8 



