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-3 f(x) y 6 3 -3 -6 3

-3 f(x) y 6 3 -3 -6 3

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Integral Calculation Exercise **5. Find the exact values of each of the integrals below.** #### Integrals (a) \(\int_{-5}^{-3} f(x) \, dx\) (b) \(\int_{-5}^{-2} f(x) \, dx\) (c) \(\int_{-3}^{-1} f(x) \, dx\) (d) \(\int_{-2}^{-1} f(x) \, dx\) (e) \(\int_{1}^{5} f(x) \, dx\) #### Graph Description The graph of the function \(f(x)\) is displayed on a coordinate plane. Key features of the graph include: - The x-axis ranges from \(-6\) to \(6\). - The y-axis ranges from \(-6\) to \(6\). - The graph consists of linear segments connecting several points. Specific points and segments of interest: - From \(x = -5\) to \(x = -3\), the graph is a horizontal line at \(y = 3\). - At \(x = -3\), the graph sharply drops down to \(x = -2\), reaching \(y = -6\). - From \(x = -2\) to \(x = -1\), the graph rises back up to \(y = 3\). - Between \(x = 1\) and \(x = 3\), the graph remains constant at \(y = 3\). - From \(x = 3\) to \(x = 4\), the graph rises to \(y = 6\). - The graph decreases linearly from \(x = 4\) to \(x = 5\), ending at near \(y = 0\). Use this graph to determine the values of the integrals by calculating the area under the curve for each specified interval.
Transcribed Image Text:### Integral Calculation Exercise **5. Find the exact values of each of the integrals below.** #### Integrals (a) \(\int_{-5}^{-3} f(x) \, dx\) (b) \(\int_{-5}^{-2} f(x) \, dx\) (c) \(\int_{-3}^{-1} f(x) \, dx\) (d) \(\int_{-2}^{-1} f(x) \, dx\) (e) \(\int_{1}^{5} f(x) \, dx\) #### Graph Description The graph of the function \(f(x)\) is displayed on a coordinate plane. Key features of the graph include: - The x-axis ranges from \(-6\) to \(6\). - The y-axis ranges from \(-6\) to \(6\). - The graph consists of linear segments connecting several points. Specific points and segments of interest: - From \(x = -5\) to \(x = -3\), the graph is a horizontal line at \(y = 3\). - At \(x = -3\), the graph sharply drops down to \(x = -2\), reaching \(y = -6\). - From \(x = -2\) to \(x = -1\), the graph rises back up to \(y = 3\). - Between \(x = 1\) and \(x = 3\), the graph remains constant at \(y = 3\). - From \(x = 3\) to \(x = 4\), the graph rises to \(y = 6\). - The graph decreases linearly from \(x = 4\) to \(x = 5\), ending at near \(y = 0\). Use this graph to determine the values of the integrals by calculating the area under the curve for each specified interval.
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