calculus
posted by AJ .
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.

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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