Question

Approximate the area of the shaded region by using the Trapezoidal Rule with n=3.

Answer 1

Let's use Trapezoidal Rule Formula

$\begin{gathered} \frac{\Delta x}{2}[f(x_0)+2f(x1)+........+2f(x_{n-1})+f\mleft(x_n\mright)] \\ \\ \Delta x=\frac{b-a}{n} \end{gathered}$

Replacing

$\Delta x=\frac{10-(-20)}{3}=10$$\begin{gathered} \frac{10}{2}[f(-20)+2f(-10)+2f(0)+f(10)] \\ \\ 5[f(-20)+2f(-10)+2f(0)+f(10)] \end{gathered}$

Replacing

$\begin{gathered} 5[30+2(20)+2(15)+25] \\ 5[30+40+30+25] \\ 25 \end{gathered}$

Answer: 25