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Find the area of the region. f(x) = 25 – x? y 30 25 20 15 10 5 -10 10

Find the area of the region. f(x) = 25 – x? y 30 25 20 15 10 5 -10 10

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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**Problem Statement:** Find the area of the region. **Function:** \( f(x) = 25 - x^2 \) **Graph Description:** This graph displays the parabola defined by the quadratic function \( f(x) = 25 - x^2 \). The parabola opens downward, with its vertex at the point (0, 25) on the y-axis. - The x-axis and y-axis are clearly marked, with the x-axis ranging from -10 to 10 and the y-axis ranging from 0 to 30. - The shaded region under the curve indicates the area that needs to be found. This shaded area extends symmetrically from \( x = -5 \) to \( x = 5 \). - The curve intersects the x-axis at \( x = -5 \) and \( x = 5 \), indicating the roots of the equation where \( f(x) = 0 \). **Objective:** Calculate the total area of the shaded region under the curve from \( x = -5 \) to \( x = 5 \).
Transcribed Image Text:**Problem Statement:** Find the area of the region. **Function:** \( f(x) = 25 - x^2 \) **Graph Description:** This graph displays the parabola defined by the quadratic function \( f(x) = 25 - x^2 \). The parabola opens downward, with its vertex at the point (0, 25) on the y-axis. - The x-axis and y-axis are clearly marked, with the x-axis ranging from -10 to 10 and the y-axis ranging from 0 to 30. - The shaded region under the curve indicates the area that needs to be found. This shaded area extends symmetrically from \( x = -5 \) to \( x = 5 \). - The curve intersects the x-axis at \( x = -5 \) and \( x = 5 \), indicating the roots of the equation where \( f(x) = 0 \). **Objective:** Calculate the total area of the shaded region under the curve from \( x = -5 \) to \( x = 5 \).
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