5. The graph of a certain function f(x) with domain [-3,3] consist of a semicircle of center (-2,0) and radius 1 and a number of line seg- ments. Find the following integrals: (a) [² f(x) dx › [²₁ f(x) dx (b) (c) * f(x) dx -3 -2 -1 0 -1 1 2 3
5. The graph of a certain function f(x) with domain [-3,3] consist of a semicircle of center (-2,0) and radius 1 and a number of line seg- ments. Find the following integrals: (a) [² f(x) dx › [²₁ f(x) dx (b) (c) * f(x) dx -3 -2 -1 0 -1 1 2 3
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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![**Exercise 5:**
The graph of a certain function \( f(x) \) with domain \([-3, 3]\) consists of a semicircle with center \((-2, 0)\) and radius 1, along with several line segments. Find the following integrals:
(a) \(\int_{-3}^{-2} f(x) \, dx\)
(b) \(\int_{-1}^{2} f(x) \, dx\)
(c) \(\int_{2}^{3} f(x) \, dx\)
(d) \(\int_{-3}^{3} f(x) \, dx\)
**Graph Explanation:**
- The graph includes a semicircle centered at \((-2, 0)\) with a radius of 1, spanning from \(x = -3\) to \(x = -1\).
- From \(x = -1\) to \(x = 0\), there is a line segment moving upward.
- From \(x = 0\) to \(x = 2\), the line segment continues with a positive slope.
- At \(x = 2\), the graph forms a peak and then descends in a straight line down to \(x = 3\).
This setup is used to find specific integrals over different intervals on the \(x\)-axis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F593e4a4c-a9fc-4231-bacd-fbc9affb1612%2F3653f150-5cf3-48f7-811d-99c3657ad9cd%2Fcz9ei84_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise 5:**
The graph of a certain function \( f(x) \) with domain \([-3, 3]\) consists of a semicircle with center \((-2, 0)\) and radius 1, along with several line segments. Find the following integrals:
(a) \(\int_{-3}^{-2} f(x) \, dx\)
(b) \(\int_{-1}^{2} f(x) \, dx\)
(c) \(\int_{2}^{3} f(x) \, dx\)
(d) \(\int_{-3}^{3} f(x) \, dx\)
**Graph Explanation:**
- The graph includes a semicircle centered at \((-2, 0)\) with a radius of 1, spanning from \(x = -3\) to \(x = -1\).
- From \(x = -1\) to \(x = 0\), there is a line segment moving upward.
- From \(x = 0\) to \(x = 2\), the line segment continues with a positive slope.
- At \(x = 2\), the graph forms a peak and then descends in a straight line down to \(x = 3\).
This setup is used to find specific integrals over different intervals on the \(x\)-axis.
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