Answer
$\approx 86.631$
Work Step by Step
Write the arc length formula such as:
$L=\int_m^n \sqrt {(x'(t))^2+(y'(t))^2+(z'(t))^2} dt$
and $L=\int_0^3 \sqrt {4t^2+9t^4+16t^6} dt$
We will have to write the Simpson's rule for $n+1=7$
$L=\int_0^7 \sqrt {4 \times t^2+9 \times t^4+16 \times t^6} dt \approx \dfrac{\triangle x}{3}[f(x_0)+4f(x_1)+2f(x_2)+4f(x_3)+2f(x_4)+4f(x_5)+f(x_6)$
Hence, we have
$L\approx \dfrac{0.5}{3}[0+4 \times (1.34629)+2(5.38516)+4 \times (15.38871)+2 \times (34.4093)+4 \times (65.4432)+111.48543] \approx 86.631$
