Posted by **AJ** on Monday, April 9, 2012 at 1:50am.

Let f be the function given by: f(x)=1/5x^5/2+x^-1/2, for all x in [1,4]. Find the length of the graph of f.

- calculus -
**Steve**, Monday, April 9, 2012 at 11:54am
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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