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hint: first find parametric equations for x and y

2007-12-10 05:38:34 · 1 answers · asked by whizkid2007 1 in Science & Mathematics Mathematics

1 answers

We have x = (y^2)/4

The elementary lenght is ds = sqrt(1 + (dx/dy)^2)) dy

dx/dy = y/2, so that ds = sqrt(1 + y^2/4) dy, to be integrated from 0 to 2. Put y/2 = sinh t, so that 1+ y^2/4 = cosh^2 t and dy = 2 cosh t dt. So, in t, we have to integrate from 0 to arc sinh 1.

We get 2 Int (0 to arcsinh 1) cosh^2 t dt= 2 *1/2 [t + 1/2 sinh (2t)] from 0 to arcsinh 1

Now, you complete the integral

2007-12-10 06:05:08 · answer #1 · answered by Steiner 7 · 0 0

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