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Find the area of the region. f(x) = 25 – x2 %3D

Find the area of the region. f(x) = 25 – x2 %3D

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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The task is to find the area of the region under the curve of the function \( f(x) = 25 - x^2 \). **Description of the Graph:** - **Function:** The graph represents the parabola defined by the function \( f(x) = 25 - x^2 \). - **Shape and Position:** The parabola opens downwards with its vertex at the point (0, 25) on the y-axis. - **Axes:** The x-axis ranges from -10 to 10, while the y-axis ranges from 0 to 30. - **Shaded Region:** The area of interest is the region above the x-axis and below the curve from \( x = -5 \) to \( x = 5 \). This is the blue-shaded area. The goal is to calculate the area of this shaded region using integration techniques. This involves evaluating the definite integral of \( f(x) \) from \( x = -5 \) to \( x = 5 \).
Transcribed Image Text:The task is to find the area of the region under the curve of the function \( f(x) = 25 - x^2 \). **Description of the Graph:** - **Function:** The graph represents the parabola defined by the function \( f(x) = 25 - x^2 \). - **Shape and Position:** The parabola opens downwards with its vertex at the point (0, 25) on the y-axis. - **Axes:** The x-axis ranges from -10 to 10, while the y-axis ranges from 0 to 30. - **Shaded Region:** The area of interest is the region above the x-axis and below the curve from \( x = -5 \) to \( x = 5 \). This is the blue-shaded area. The goal is to calculate the area of this shaded region using integration techniques. This involves evaluating the definite integral of \( f(x) \) from \( x = -5 \) to \( x = 5 \).
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