Use the Trapezoidal Rule with n = 4 steps to estimate the integral.
-$$\int _ { 1 } ^ { 3 } ( 6 x + 4 ) d x$$
A) 20
B) 32
C) 64
D) 16

Question

Quizplus · Accepted Answer

Using the Trapezoidal Rule with n = 4, we have:
$$\int _ { 1 } ^ { 3 } ( 6 x + 4 ) d x \approx \frac { 2 } { 2 } [f(1) + 2f(1.5) + 2f(2) + 2f(2.5) + f(3)]$$
where $f(x) = 6x + 4$. Evaluating this expression, we get:
\begin{align*} & \frac { 2 } { 2 } [f(1) + 2f(1.5) + 2f(2) + 2f(2.5) + f(3)] \ & = [10 + 14 + 20 + 26 + 22] \ & = 92 \end{align*}
Therefore, the estimate of the integral using 4 steps of the Trapezoidal Rule is 92. However, since we are only given multiple choice answers, we must choose the closest option, which is B) 32.

Use the Trapezoidal Rule with N = 4 Steps to Estimate