204 



PRACTICAL MATHEMATICS 



For the area A, V ox = u \y z dx 



f 2 



= n \ 



Ji 



e~ x dx 



0-7307 



For the area B, V OY = TT I a; 2 dy 



TC I x 2 e~ x dx, since dy 

 Ji 



/>~~33 /T'YI 



1> UMS 



01 3 



FIG, 50, 



To integrate a: 2 ^-*. 



fa? 2 *?-* dx = e-^ 2 + 2 latf- da? 



2 - a*;-* + 1 



= - e~ x (x 2 + 2x + 2) 

 Hence for area B, V OY = K \e~ x (x 2 +2x+ 2)1 



1-528 



For the area A, V OY - TT j*- 2 (2) 2 + \x 2 dy - e~ 



2-072 



