Solve the problem.
-Suppose that the accompanying table shows the velocity of a car every second for 8 seconds. Use the Trapezoidal Rule to approximate the distance traveled by the car in the 8 seconds. Round your answer to the nearest tenth if necessary.
$\begin{array}{l|l}
\text { Time (sec) } & \text { Velocity (ft/sec) } \
\hline 0 & 17 \
1 & 18 \
2 & 19 \
3 & 21 \
4 & 20 \
5 & 22 \
6 & 19 \
7 & 17 \
8 & 18
\end{array}$

A) 153.5 ft
B) 171 ft
C) 233.5 ft
D) 307 ft

Question

Solve the problem.
-Suppose that the accompanying table shows the velocity of a car every second for 8 seconds. Use the Trapezoidal Rule to approximate the distance traveled by the car in the 8 seconds. Round your answer to the nearest tenth if necessary.
$\begin{array}{l|l}
\text { Time (sec) } & \text { Velocity (ft/sec) } \
\hline 0 & 17 \
1 & 18 \
2 & 19 \
3 & 21 \
4 & 20 \
5 & 22 \
6 & 19 \
7 & 17 \
8 & 18
\end{array}$

A) 153.5 ft
B) 171 ft
C) 233.5 ft
D) 307 ft

Quizplus · Accepted Answer

The Trapezoidal Rule for approximating the integral (in this case, the distance traveled) is given by the formula: $\frac{h}{2} [f(x_0) + 2f(x_1) + 2f(x_2) + \ldots + 2f(x_{n-1}) + f(x_n)]$, where $h$ is the step size (in this case, 1 second), $f(x_i)$ represents the velocity at time $x_i$, and $n$ is the number of intervals (in this case, 8). Applying this to the given velocities, we get: $\frac{1}{2} [17 + 2(18 + 19 + 21 + 20 + 22 + 19) + 17 + 18] = \frac{1}{2} [17 + 36 + 38 + 42 + 40 + 44 + 38 + 17 + 18] = \frac{1}{2} [290] = 145$. However, this calculation seems to have been misunderstood in the explanation. Correctly applying the Trapezoidal Rule should give us: $\frac{1}{2} [17 + 2(18 + 19 + 21 + 20 + 22 + 19 + 17) + 18] = \frac{1}{2} [17 + 2(156) + 18] = \frac{1}{2} [347] = 173.5$. It appears there was a mistake in the calculation provided in the explanation. The correct application of the Trapezoidal Rule indeed involves summing the first and last values once and the intermediate values twice, then multiplying by half the step size. Given the options provided and acknowledging a mistake in the initial calculation explanation, the correct approach still involves using the Trapezoidal Rule correctly with the given data. The correct answer should reflect the sum of the velocities according to the Trapezoidal Rule formula, indicating a mistake in the initial response provided.

Solve the Problem A) 1535 Ft B) 171 Ft C) 233

Solve the Problem A) 1535 Ft
B) 171 Ft
C) 233