Determine the arc length of the following on the specified interval:
y=1/2x^3/2 , x=0, x=4
s = ∫[0,4] √(1+y'^2) dx
= ∫[0,4] √(1+(3/4 x^1/2)^2) dx
= ∫[0,4] √(1+9x/16) dx
= 1/54 (9x+16)^(3/2) [0,4]
= 4/27 (13√13 - 8)
y=1/2x^3/2 , x=0, x=4
= ∫[0,4] √(1+(3/4 x^1/2)^2) dx
= ∫[0,4] √(1+9x/16) dx
= 1/54 (9x+16)^(3/2) [0,4]
= 4/27 (13√13 - 8)