Use Simpson's Rule with n = 4 to estimate the length of the arc of the curve with equations $x = \sqrt { t } , y = \frac { 4 } { t } , z = t ^ { 2 } + 1$ , from $( 1,4,2 )$ to $( 2,1,17 )$ . Round your answer to four decimal places.
A) $14.824$
B) $7.2041$
C) $7.4106$
D) $6.5706$
E) None of these

Question

Quizplus · Accepted Answer

We start by calculating the step size, $h=\frac{b-a}{n}=\frac{2-1}{4}=0.25$. Then we use Simpson's Rule:
$$\begin{aligned} \int_a^b ds &= \frac{h}{3}[f(a)+4f(a+h)+2f(a+2h)+4f(a+3h)+f(b)]\ &\approx \frac{0.25}{3}\left[f(1)+4f(1.25)+2f(1.5)+4f(1.75)+f(2)ight] \ &\approx 7.4106 \end{aligned}$$
Therefore, the estimated length of the curve is approximately $7.4106$.

Use Simpson's Rule with N = 4 to Estimate the Length