Posted by AJ on Monday, April 9, 2012 at 1:50am.
f = 1/5 x^5/2 + x^-1/2
df/dx = 1/2 x^3/2 - 1/2 x^-3/2
ds/dx = sqrt(1+(1/2 x^3/2 - 1/2 x^-3/2)^2)
= 1/2 x^3/2 + 1/2 x^-3/2
s = ∫[1,4] 1/2 x^3/2 + 1/2 x^-3/2 dx
= (1/5 x^5/2 - x^-1/2) [1,4]
= [(32/5 - 1/2)-(1/5 - 1)]
= [59/10 + 8/10]
= 67/10
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