LENGTHS OF CURVES 



269 



I f 55 T 

 = 4 a^efe 



W Jw 



= 12-05 



Example 2. Find the length of the arc of the curve y* 

 between the limits x = 2 and x = 4. 



The limits for y are t/ = 4 and / = 4\/2. 



Now 



V 



x = ^ 



o 



t y z = 16 sinh 2 



d VlQ + y 2 = 4 cosh 



dy = 4 cosh d0 



5=4 Icosh 2 dQ 

 = 2 f(l + cosh 20) d0 



2 9 + s sinh 20 



1 



