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

Replacing

`\Delta x=(10-(-20))/(3)=10`
`\begin{gathered} (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