3. On paper please ## Approximating Definite Integrals Using the Trapezoidal Rule### Problem StatementGiven the graph of $ f(x) $, set up the approximation of the definite integral using the Trapezoidal Rule with $ n = 4 $. In your work, include your estimated y-values.### Integral to Approximate\[\int_{0}^{4} f(x) \, dx\]### Graph ExplanationThe graph provided is a plot of the function $ f(x) $ over the interval $[0, 4]$. The x-axis ranges from approximately $-4$ to $4$, while the y-axis ranges from $-4$ to $8$. The curve indicates $ f(x) $ has both increasing and decreasing intervals, featuring a significant peak and trough within the specified range.### Steps to Use the Trapezoidal Rule1. **Divide the Interval**: The interval $[0, 4]$ is divided into $ n = 4 $ equal parts, each of width $ \Delta x = 1 $.2. **Estimate y-values**: For each subinterval endpoint, estimate the y-value (height) from the graph.3. **Apply the Trapezoidal Rule Formula**: \[ \int_{0}^{4} f(x) \, dx \approx \frac{\Delta x}{2} \left[ f(x_0) + 2f(x_1) + 2f(x_2) + 2f(x_3) + f(x_4) \right] \] where $ x_0, x_1, x_2, x_3, x_4 $ are the endpoints of the subintervals.4. **Calculate the Approximation**: Insert the estimated y-values into the formula to find the approximate value of the integral.

Given the following graph of f(x), set up the approximation of the definite integral using the Trapezoidal Rule and n = 4. In your work, include your estimated y-values. Graph: -2 Integral: f(x)dx 2 2

Given the following graph of f(x), set up the approximation of the definite integral using the Trapezoidal Rule and n = 4. In your work, include your estimated y-values. Graph: -2 Integral: f(x)dx 2 2

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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