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

Vrushali Raut asked Jul 25, 2023

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27 votes

Vrushali Raut asked Jul 25, 2023

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16 votes

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

Wamfous answered Jul 31, 2023

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