8.8. 2 **Evaluating Definite Integrals Using the Midpoint Rule**### Problem Statement:Compute the following estimate of \( \int_{0}^{8} f(x) \, dx \) using the graph in the figure.M(4)### Figure Description:The figure shows the graph of the function \( y = f(x) \), plotted between \( x = 0 \) and \( x = 10 \). The graph has a curvy shape passing through several points on the grid. Key points where the function is evaluated are visible on the plot.### Estimation Using the Midpoint Rule:The Midpoint Rule for \( n \) subintervals is given by:\[ M(n) = \Delta x \left[ f\left(m_1\right) + f\left(m_2\right) + \ldots + f\left(m_n\right) \right] \]where \( \Delta x \) is the width of each subinterval, and \( m_i \) represents the midpoint of each subinterval.For this problem, the interval is from 0 to 8, and we need to estimate using 4 subintervals (\( n = 4 \)).### Calculation:1. Determine the width of each subinterval, \( \Delta x \):\[ \Delta x = \frac{8 - 0}{4} = 2 \]2. Identify the midpoints of each subinterval:- Subinterval 1: [0, 2], Midpoint at \( x = 1 \)- Subinterval 2: [2, 4], Midpoint at \( x = 3 \)- Subinterval 3: [4, 6], Midpoint at \( x = 5 \)- Subinterval 4: [6, 8], Midpoint at \( x = 7 \)3. Evaluate the function at each midpoint:- \( f(1) \approx 2 \) (based on the graph)- \( f(3) \approx 6 \) - \( f(5) \approx 4 \)- \( f(7) \approx 8 \)4. Apply the Midpoint Rule formula:\[ M(4) = 2 \left[ f(1) + f(3) + f(5) + f(7) \right] \]\[ M(4

Name: 8.8. 2 **Evaluating Definite Integrals Using the Midpoint Rule**##
Uploaded: 2024-03-20T07:06:41.000Z
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Description: 8.8. 2 **Evaluating Definite Integrals Using the Midpoint Rule**### Problem Statement:Compute the following estimate of \( \int_{0}^{8} f(x) \, dx \) using the graph in the figure.M(4)### Figure Description:The figure shows the graph of the funct