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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Question
![**Problem:**
Find the area of the region bounded above by \( y = -x^2 + 5 \) and below by \( y = 1 \).
**Graph Description:**
The graph shows a parabola represented by the equation \( y = -x^2 + 5 \) with its vertex at the point (0, 5). The parabola opens downwards, intersecting the x-axis at points (-√5, 0) and (√5, 0). A horizontal line is drawn at \( y = 1 \). The shaded region between the parabola and the horizontal line represents the area that needs to be calculated.
**Choices:**
- **a.** \( \frac{8}{3} \)
- **b.** \( \frac{16}{3} \)
- **c.** \( \frac{32}{3} \) (correct answer, selected)
- **d.** 36](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb111f9a2-d607-44d0-9cf1-983102308b09%2F61e1773e-e017-453d-a20e-92884cd67418%2Fniqejem_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem:**
Find the area of the region bounded above by \( y = -x^2 + 5 \) and below by \( y = 1 \).
**Graph Description:**
The graph shows a parabola represented by the equation \( y = -x^2 + 5 \) with its vertex at the point (0, 5). The parabola opens downwards, intersecting the x-axis at points (-√5, 0) and (√5, 0). A horizontal line is drawn at \( y = 1 \). The shaded region between the parabola and the horizontal line represents the area that needs to be calculated.
**Choices:**
- **a.** \( \frac{8}{3} \)
- **b.** \( \frac{16}{3} \)
- **c.** \( \frac{32}{3} \) (correct answer, selected)
- **d.** 36
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