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...
Related questions
Question
How would you solve problem 12?

Transcribed Image Text:### Transcription for an Educational Website
#### Calculating Definite Integrals
**Exercises:**
8. Evaluate the integral \( \int_{0}^{2} |x^3 - 1| \, dx \).
10. Evaluate the integral \( \int_{-1}^{1} |3x - 2| \, dx \).
#### Solving Equations for Shaded Regions
Given Functions:
- \( f(x) = x^3 + 3x^2 - 9x - 12 \)
- \( g(x) = 4x + 3 \)
### Detailed Description of Graphs
The graph features two functions, \( f(x) \) and \( g(x) \), plotted on a coordinate system. The function \( f(x) = x^3 + 3x^2 - 9x - 12 \) appears as a cubic curve, while \( g(x) = 4x + 3 \) is a straight line. The graph displays the following key points:
- Intersection Points: The graph shows points where the functions intersect, located at approximately \((-5, -17)\) and \((3, 15)\).
- Axes: The x-axis ranges from -6 to 4 and the y-axis from -20 to 20.
- Shaded Region: There is a shaded area between the two curves, indicating the region between the functions \( f(x) \) and \( g(x) \).
Find the solutions for these intersecting equations:
15. \( y = \)
16. \( y = \)
17. \( y = \)
19. \( y = \)
21. \( y = \)
23. \( y = \)
25. \( y = \)
27. \( y = \)
28. \( y = \)
29. \( y = \)
30. \( f(x) \)
31. \( f(x) \)
32. \( y = \)
33. \( y = \)
The graph helps visualize the intersection and the areas under discussion, providing insight into solving the integrals and analyzing the relationship between the two functions.
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