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EXAMPLE 4 Find the arc length for the curve y = 3x2 In(x) taking Po(l, 3) as the starting point. 24 SOLUTION If f(x) = 3x2 T In(x), then 1, 24,x 1 24x = 1+ 36x2 - 0.5 + 1 = 36x2 + 0.5+ 2 576x 1 1 6x + 24x Thus the arc length is given by s(x) = 1 For instance, the arc length along the curve from (It 3) to (3/ f(3)) is s(3) = + In(3) 3 In(3) 45.0578 X (rounded to four decimal places).