Show that to find the length of an arc of the parabola one needs to determine
the area under the hype
ola .

005_zk-rez0zonl.pdf

Question

Show that to find the length of an arc of the parabola     one needs to determine the area under the hypeola         .

David · Accepted Answer

Show that to find the length of an arc of the parabola y=x2 one needs to determine the area 
under the hyperbola y2 – 4x2 = 1. 
Ans) Length of arc = ʃa
b (1 + f’(x)2)0.5 dx 
   ( )  
  
  
     
 (1 + f’(x)2)0.5  = (1+(2x)2)0.5 = (1+4x2)0.5 
 Length of arc = ʃa
b (1 + f’(x)2)0.

Show that to find the length of an arc of the parabola one needs to determine the area under the hyperbola .

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