The graph of f consists of line segments and a semicircle, as shown in the figure. Evaluate each definite integral by using geometric formulas. (4, 2) 1+ 6 (-4, – 1)
The graph of f consists of line segments and a semicircle, as shown in the figure. Evaluate each definite integral by using geometric formulas. (4, 2) 1+ 6 (-4, – 1)
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 graph of \( f \) consists of line segments and a semicircle, as shown in the figure. Evaluate each definite integral by using geometric formulas.
**Graph Description:**
- The graph has the x-axis and y-axis intersecting at the origin.
- There is a semicircle centered on the x-axis with its bottom at \((0, -1)\) and its diameter from \((-2, 0)\) to \((2, 0)\).
- Line segments form the rest of the graph:
- A line segment descends from \((-4, -1)\) to \((-2, 0)\).
- A line segment ascends from \((2, 0)\) to \((4, 2)\).
- A line segment descends again from \((4, 2)\) to \((6, 0)\).
**Integral to Evaluate:**
- \( \int_{-4}^{6} [f(x) + 2] \, dx \)
The integral evaluates to \(2(11 - \pi)\), which is marked incorrect, suggesting further evaluation is needed for verification.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81a2b3ad-739c-4a46-a1a9-6fcc88ba4ac8%2F872150d4-223d-471e-b4e7-4a3060084289%2F8gnzxvb_processed.png&w=3840&q=75)
Transcribed Image Text:The graph of \( f \) consists of line segments and a semicircle, as shown in the figure. Evaluate each definite integral by using geometric formulas.
**Graph Description:**
- The graph has the x-axis and y-axis intersecting at the origin.
- There is a semicircle centered on the x-axis with its bottom at \((0, -1)\) and its diameter from \((-2, 0)\) to \((2, 0)\).
- Line segments form the rest of the graph:
- A line segment descends from \((-4, -1)\) to \((-2, 0)\).
- A line segment ascends from \((2, 0)\) to \((4, 2)\).
- A line segment descends again from \((4, 2)\) to \((6, 0)\).
**Integral to Evaluate:**
- \( \int_{-4}^{6} [f(x) + 2] \, dx \)
The integral evaluates to \(2(11 - \pi)\), which is marked incorrect, suggesting further evaluation is needed for verification.
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