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Find the area of the region bounded above by y = -x² + 4 and below by y = x - + 54-324 2,345 ມາຜ່າ !

Find the area of the region bounded above by y = -x² + 4 and below by y = x - + 54-324 2,345 ມາຜ່າ !

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 bounded above by \( y = -x^2 + 4 \) and below by \( y = x - 2 \). ### Graph Explanation The graph provided depicts the parabolic curve \( y = -x^2 + 4 \) and the straight line \( y = x - 2 \). These two equations intersect, forming a region that is shaded in the graph. The parabolic curve opens downwards with its vertex at the point (0,4) and the straight line intersects the y-axis at -2 and has a slope of 1. ### Calculations and Options To find the area between the curves, we need to identify the x-coordinates of the points of intersection of \( y = -x^2 + 4 \) and \( y = x - 2 \) and integrate the difference of the functions over that interval. ### Answer Choices - \( \frac{125}{6} \) - \( \frac{375}{16} \) - \( \frac{375}{13} \) - 375
Transcribed Image Text:### Problem Statement Find the area of the region bounded above by \( y = -x^2 + 4 \) and below by \( y = x - 2 \). ### Graph Explanation The graph provided depicts the parabolic curve \( y = -x^2 + 4 \) and the straight line \( y = x - 2 \). These two equations intersect, forming a region that is shaded in the graph. The parabolic curve opens downwards with its vertex at the point (0,4) and the straight line intersects the y-axis at -2 and has a slope of 1. ### Calculations and Options To find the area between the curves, we need to identify the x-coordinates of the points of intersection of \( y = -x^2 + 4 \) and \( y = x - 2 \) and integrate the difference of the functions over that interval. ### Answer Choices - \( \frac{125}{6} \) - \( \frac{375}{16} \) - \( \frac{375}{13} \) - 375
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