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ind the area of the region. See Examples 1, 2, 3, and 4. 7(x³ - x) f(x) g(x) = 0 = -2 10 00 6 - 2 -2 -4 -6 -8 -10L g 2

ind the area of the region. See Examples 1, 2, 3, and 4. 7(x³ - x) f(x) g(x) = 0 = -2 10 00 6 - 2 -2 -4 -6 -8 -10L g 2

Advanced Engineering Mathematics
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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**Finding the Area of the Region** To find the area of the region, refer to the Examples 1, 2, 3, and 4. Given Functions: - \( f(x) = 7(x^3 - x) \) - \( g(x) = 0 \) **Graph Explanation:** The graph shows two functions, \( f(x) \) and \( g(x) \): 1. **Function \( f(x) \)**: - This is a cubic function represented by \( f(x) = 7(x^3 - x) \). - It passes through the x-axis and creates a wave-like shape with peaks and valleys. 2. **Function \( g(x) \)**: - This is a constant function, \( g(x) = 0 \), which is the x-axis itself. **Shaded Region:** - The region shaded in blue represents the area between the curve of \( f(x) \) and the x-axis (where \( g(x) = 0 \)). - The shaded area is between approximately \( x = -1.7 \) to \( x = 1.4 \). **Objective:** - Calculate the area of this region by integrating the function \( f(x) \) over the specified interval where it lies above the x-axis.
Transcribed Image Text:**Finding the Area of the Region** To find the area of the region, refer to the Examples 1, 2, 3, and 4. Given Functions: - \( f(x) = 7(x^3 - x) \) - \( g(x) = 0 \) **Graph Explanation:** The graph shows two functions, \( f(x) \) and \( g(x) \): 1. **Function \( f(x) \)**: - This is a cubic function represented by \( f(x) = 7(x^3 - x) \). - It passes through the x-axis and creates a wave-like shape with peaks and valleys. 2. **Function \( g(x) \)**: - This is a constant function, \( g(x) = 0 \), which is the x-axis itself. **Shaded Region:** - The region shaded in blue represents the area between the curve of \( f(x) \) and the x-axis (where \( g(x) = 0 \)). - The shaded area is between approximately \( x = -1.7 \) to \( x = 1.4 \). **Objective:** - Calculate the area of this region by integrating the function \( f(x) \) over the specified interval where it lies above the x-axis.
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