198 



PRACTICAL MATHEMATICS 



Example 3. Find the area enclosed by the curve xy = 1 and 

 the straight line 4t/ + Qx = 11. 



o 



2 



FIG, 46, 



The points of intersection P and Q have for their co-ordinates 

 the values of x and y, which satisfy the equations xy = I and 

 3x = 11. 



\ (11 -te)-l 



Then 



and 



- 3# 2 = 4 

 4 = 

 a? = 0-408, x = 3-259 



Area = \y dx where y is the length of ordinate between the 



line and the curve. 



Hence area = nrU 1 Sx ) \ dx 



3 I 3 ' 



rv\ _ ^l 1 * . Ir^Of -T 1 I 

 rT Ofi 1 "^ I 



8 Jo- 



3-259 

 O' 408 



= ^(3-259 - 0-408) - ?(3-259 2 - 0-408 2 ) - log, jj|jig 



= 7-840 - 3-291 - 2-078 

 = 1-841 



