you might need: calculator\napproximate the area between h(x) and the x-axis from x = 0 to x = 3 using a…

Explanation:

Step1: Find subinterval width

The interval is $[0,3]$ with 3 subdivisions. $\Delta x = \frac{3-0}{3} = 1$

Step2: Identify function values

From the graph: $h(0)=7$, $h(1)=3$, $h(2)=1$, $h(3)=2$

Step3: Apply trapezoidal rule

The formula is $T(n)=\frac{\Delta x}{2}\left[h(x_0)+2h(x_1)+2h(x_2)+h(x_3)\right]$ $$T(3)=\frac{1}{2}\left[7 + 2(3) + 2(1) + 2\right]$$

Step4: Calculate the sum

First compute inside the brackets: $7 + 6 + 2 + 2 = 17$ Then multiply by $\frac{1}{2}$: $\frac{1}{2} \times 17 = 8.5$

Answer:

$8.5$