# Section 14.9 - Area Between Curves ## Problems and Solutions ### Exercises 8. \( y = 2 - x^2 \) 9. \( y = 9 - x^2 \), \( x = 0 \) 10. \( y = 4 \), \( x = 1 \), \( x = 2 \) 11. \( y = x^3 - x \) 12. \( y = 1/x \), \( x = 1 \), \( x = 3 \) 13. \( y = \frac{(x - 1)^2}{x} \), \( x = 2 \), \( x = 3 \) 14. \( y = x^3 - 4x \), \( x = 0 \) 15. \( y = x^2 + x - 9 \), \( x = 0 \) 16. \( y = 4 - x^2 \), \( x = 1 \), \( y = 3 \) 17. \( y = x^{1/2} \), \( x = 1 \), \( x = 4 \) 18. \( y = x^{1/3} \), \( x = 0 \), \( x = 1 \) 19. \( y = e^{1 + x} \), \( x = 0 \), \( x = 1 \) 20. \( y = \sqrt{x} \), \( x = 1 \), \( x = 2 \) 21. \( y = x^2 - x \), \( x = 2 \) 22. \( y = 2 - x^2 \), \( x = 1 \) 23. \( y = 6x - x^2 \), \( x = 3 \) 24. \( y = -x^2 + 2x \), \( x = 0 \), \( x = 4 \) 25. Given that \[ f(x) = \begin{cases} 3x^2 & \text{if } 0 \leq x < 2 \\ 16 - x^2 & \text{if } x \geq 2 \end{cases} \] Determine the area of the region bounded by the graph of \( y = f
# Section 14.9 - Area Between Curves ## Problems and Solutions ### Exercises 8. \( y = 2 - x^2 \) 9. \( y = 9 - x^2 \), \( x = 0 \) 10. \( y = 4 \), \( x = 1 \), \( x = 2 \) 11. \( y = x^3 - x \) 12. \( y = 1/x \), \( x = 1 \), \( x = 3 \) 13. \( y = \frac{(x - 1)^2}{x} \), \( x = 2 \), \( x = 3 \) 14. \( y = x^3 - 4x \), \( x = 0 \) 15. \( y = x^2 + x - 9 \), \( x = 0 \) 16. \( y = 4 - x^2 \), \( x = 1 \), \( y = 3 \) 17. \( y = x^{1/2} \), \( x = 1 \), \( x = 4 \) 18. \( y = x^{1/3} \), \( x = 0 \), \( x = 1 \) 19. \( y = e^{1 + x} \), \( x = 0 \), \( x = 1 \) 20. \( y = \sqrt{x} \), \( x = 1 \), \( x = 2 \) 21. \( y = x^2 - x \), \( x = 2 \) 22. \( y = 2 - x^2 \), \( x = 1 \) 23. \( y = 6x - x^2 \), \( x = 3 \) 24. \( y = -x^2 + 2x \), \( x = 0 \), \( x = 4 \) 25. Given that \[ f(x) = \begin{cases} 3x^2 & \text{if } 0 \leq x < 2 \\ 16 - x^2 & \text{if } x \geq 2 \end{cases} \] Determine the area of the region bounded by the graph of \( y = f
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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![# Section 14.9 - Area Between Curves
## Problems and Solutions
### Exercises
8. \( y = 2 - x^2 \)
9. \( y = 9 - x^2 \), \( x = 0 \)
10. \( y = 4 \), \( x = 1 \), \( x = 2 \)
11. \( y = x^3 - x \)
12. \( y = 1/x \), \( x = 1 \), \( x = 3 \)
13. \( y = \frac{(x - 1)^2}{x} \), \( x = 2 \), \( x = 3 \)
14. \( y = x^3 - 4x \), \( x = 0 \)
15. \( y = x^2 + x - 9 \), \( x = 0 \)
16. \( y = 4 - x^2 \), \( x = 1 \), \( y = 3 \)
17. \( y = x^{1/2} \), \( x = 1 \), \( x = 4 \)
18. \( y = x^{1/3} \), \( x = 0 \), \( x = 1 \)
19. \( y = e^{1 + x} \), \( x = 0 \), \( x = 1 \)
20. \( y = \sqrt{x} \), \( x = 1 \), \( x = 2 \)
21. \( y = x^2 - x \), \( x = 2 \)
22. \( y = 2 - x^2 \), \( x = 1 \)
23. \( y = 6x - x^2 \), \( x = 3 \)
24. \( y = -x^2 + 2x \), \( x = 0 \), \( x = 4 \)
25. Given that
\[
f(x) = \begin{cases}
3x^2 & \text{if } 0 \leq x < 2 \\
16 - x^2 & \text{if } x \geq 2
\end{cases}
\]
Determine the area of the region bounded by the graph of \( y = f](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e2d6f28-e3d7-414c-b1d4-a752131175c2%2Fdeb5093c-c93d-4b5f-92be-ba858d02de8b%2Flz6zjv.jpeg&w=3840&q=75)
Transcribed Image Text:# Section 14.9 - Area Between Curves
## Problems and Solutions
### Exercises
8. \( y = 2 - x^2 \)
9. \( y = 9 - x^2 \), \( x = 0 \)
10. \( y = 4 \), \( x = 1 \), \( x = 2 \)
11. \( y = x^3 - x \)
12. \( y = 1/x \), \( x = 1 \), \( x = 3 \)
13. \( y = \frac{(x - 1)^2}{x} \), \( x = 2 \), \( x = 3 \)
14. \( y = x^3 - 4x \), \( x = 0 \)
15. \( y = x^2 + x - 9 \), \( x = 0 \)
16. \( y = 4 - x^2 \), \( x = 1 \), \( y = 3 \)
17. \( y = x^{1/2} \), \( x = 1 \), \( x = 4 \)
18. \( y = x^{1/3} \), \( x = 0 \), \( x = 1 \)
19. \( y = e^{1 + x} \), \( x = 0 \), \( x = 1 \)
20. \( y = \sqrt{x} \), \( x = 1 \), \( x = 2 \)
21. \( y = x^2 - x \), \( x = 2 \)
22. \( y = 2 - x^2 \), \( x = 1 \)
23. \( y = 6x - x^2 \), \( x = 3 \)
24. \( y = -x^2 + 2x \), \( x = 0 \), \( x = 4 \)
25. Given that
\[
f(x) = \begin{cases}
3x^2 & \text{if } 0 \leq x < 2 \\
16 - x^2 & \text{if } x \geq 2
\end{cases}
\]
Determine the area of the region bounded by the graph of \( y = f
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