AND ON DEFINITE INTEGRATION. 483 
20 
of the integral | .log. # dx, of which each term 
11 
is readily computed. I may, however, state that 
Professor De Morgan, after taking of his series 
© 
six terms, which are much more difficult to calcu- 
late than those in the series above given, makes 
an approximation which is true only to the sixth 
place of decimals. The series, which he has 
given for the purpose of approximating to the 
value of the definite integral, is expressed in 
terms of the function and its successive finite 
differences. 
Ex. 2.—Required to approximate to | & 
which we know to be log. w. 
I III 
en 2) ay f(v)= -S3 a= = ; 
2.3.4.5 
;=— &e., &e. If we substitute these 
z£ 
f («)=- 
values in equation (15), and restore the values 
of A, B, &c., we shall have 
tind pn) a per) + Bes he... (17) 
