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Find the area under the graph of g over [-2,3]. (-x² +5, for x ≤ 0, x + 5, for x > 0 3. g(x) = 4. g(x) = (x² + 4, for x ≤ 0, 14 - x, for x > 0

Find the area under the graph of g over [-2,3]. (-x² +5, for x ≤ 0, x + 5, for x > 0 3. g(x) = 4. g(x) = (x² + 4, for x ≤ 0, 14 - x, for x > 0

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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Find the area under the graph over [-2,3] Question 3)
**Chapter 4: Integration** ### 4.4 Exercise Set **Find the area under the graph of f over \([1, 5]\).** 1. \( f(x) = \begin{cases} x + 5, & \text{for } x \leq 4 \\ 11 - \frac{1}{2}x, & \text{for } x > 4 \end{cases} \) 2. \( f(x) = \begin{cases} 2x + 1, & \text{for } x \leq 3 \\ 10 - x, & \text{for } x > 3 \end{cases} \) **Find the area under the graph of g over \([-2, 3]\).** 3. \( g(x) = \begin{cases} -x^2 + 5, & \text{for } x \leq 0 \\ x + 5, & \text{for } x > 0 \end{cases} \) 4. \( g(x) = \begin{cases} x^2 + 4, & \text{for } x \leq 0 \\ 4 - x, & \text{for } x > 0 \end{cases} \) **Find the area under the graph of f over \([-6, 4]\).** 5. \( f(x) = \begin{cases} -x - 1, & \text{for } x < -1 \\ -x^2 + 4x + 5, & \text{for } x \geq -1 \end{cases} \) 6. \( f(x) = \begin{cases} -x^2 - 6x + 8, & \text{for } x < 1 \\ 2x - 1, & \text{for } x \geq 1 \end{cases} \) **Find the area represented by each definite integral.** 7. \( \int_{-3}^{4} |x^3| \, dx \) 8. \( \int_{0}^{2} |x^3 - 1| \, dx \) 9. \( \int_{0}^{4} |x - 3| \, dx \)
Transcribed Image Text:**Chapter 4: Integration** ### 4.4 Exercise Set **Find the area under the graph of f over \([1, 5]\).** 1. \( f(x) = \begin{cases} x + 5, & \text{for } x \leq 4 \\ 11 - \frac{1}{2}x, & \text{for } x > 4 \end{cases} \) 2. \( f(x) = \begin{cases} 2x + 1, & \text{for } x \leq 3 \\ 10 - x, & \text{for } x > 3 \end{cases} \) **Find the area under the graph of g over \([-2, 3]\).** 3. \( g(x) = \begin{cases} -x^2 + 5, & \text{for } x \leq 0 \\ x + 5, & \text{for } x > 0 \end{cases} \) 4. \( g(x) = \begin{cases} x^2 + 4, & \text{for } x \leq 0 \\ 4 - x, & \text{for } x > 0 \end{cases} \) **Find the area under the graph of f over \([-6, 4]\).** 5. \( f(x) = \begin{cases} -x - 1, & \text{for } x < -1 \\ -x^2 + 4x + 5, & \text{for } x \geq -1 \end{cases} \) 6. \( f(x) = \begin{cases} -x^2 - 6x + 8, & \text{for } x < 1 \\ 2x - 1, & \text{for } x \geq 1 \end{cases} \) **Find the area represented by each definite integral.** 7. \( \int_{-3}^{4} |x^3| \, dx \) 8. \( \int_{0}^{2} |x^3 - 1| \, dx \) 9. \( \int_{0}^{4} |x - 3| \, dx \)
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