3 where is an antiderivative of f. Two-step approach for using FTC I to evaluate the definite integral Compute - Evaluate f(x)dx = F(x) + C. f(x) dx = F(x) = F(b) - F(a). b f(x)dx: Antiderivative formulas are helpful for evaluating definite integrals. See the summary in Section 5.3 and the table of integrals in this text's endleaf. WHITE 300 "x5" EXERCISES initary Questions Suppose that F'(x) = f(x) and F(0)=3, F(2) = 7. What is the area under y = f(x) over [0,2] if f(x) ≥ 0? What is the graphical interpretation of F(2) F(0) if f(x) takes on positive and negative values? Suppose that f is a negative function with antiderivative F such that 7 and F(3)=4. What is the area (a positive number) between the is and the graph of ƒ over [1,3]? ercises Exercises 1-4, sketch the region under the graph of the function and ind its area using FTC I - [0,1] 1 = [1,2] 3. Are the following statements true or false? Explain. (a) FTC I is valid only for positive functions. (b) To use FTC I, you have to choose the right antiderivative. (c) If you cannot find an antiderivative of f, then the definite integral does not exist. 4. Evaluate ef f'(x)dx, where ƒ is differentiable and f(2) = f(9)=4. 7. (4x-9x²) dx 8. u² du 2. f(x)=2x-x², [0,2] 9. (12x³ +3x²-4x)dx 10. (10x+3x5) dx 4. f(x)=cosx, [0,4] 11 21³-61³) dr 12. 6. 2 2dx 13. √ydy Exercises 5-40, evaluate the integral using FTC 1. 5. Idx 14. L • (5u4 x4/3 dx en th a REV6
3 where is an antiderivative of f. Two-step approach for using FTC I to evaluate the definite integral Compute - Evaluate f(x)dx = F(x) + C. f(x) dx = F(x) = F(b) - F(a). b f(x)dx: Antiderivative formulas are helpful for evaluating definite integrals. See the summary in Section 5.3 and the table of integrals in this text's endleaf. WHITE 300 "x5" EXERCISES initary Questions Suppose that F'(x) = f(x) and F(0)=3, F(2) = 7. What is the area under y = f(x) over [0,2] if f(x) ≥ 0? What is the graphical interpretation of F(2) F(0) if f(x) takes on positive and negative values? Suppose that f is a negative function with antiderivative F such that 7 and F(3)=4. What is the area (a positive number) between the is and the graph of ƒ over [1,3]? ercises Exercises 1-4, sketch the region under the graph of the function and ind its area using FTC I - [0,1] 1 = [1,2] 3. Are the following statements true or false? Explain. (a) FTC I is valid only for positive functions. (b) To use FTC I, you have to choose the right antiderivative. (c) If you cannot find an antiderivative of f, then the definite integral does not exist. 4. Evaluate ef f'(x)dx, where ƒ is differentiable and f(2) = f(9)=4. 7. (4x-9x²) dx 8. u² du 2. f(x)=2x-x², [0,2] 9. (12x³ +3x²-4x)dx 10. (10x+3x5) dx 4. f(x)=cosx, [0,4] 11 21³-61³) dr 12. 6. 2 2dx 13. √ydy Exercises 5-40, evaluate the integral using FTC 1. 5. Idx 14. L • (5u4 x4/3 dx en th a REV6
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
Can you explain question 7 for me
![3
where is an antiderivative of f.
Two-step approach for using FTC I to evaluate the definite integral
Compute
- Evaluate
f(x)dx = F(x) + C.
f(x) dx = F(x) = F(b) - F(a).
b
f(x)dx:
Antiderivative formulas are helpful for evaluating definite integrals. See the summary
in Section 5.3 and the table of integrals in this text's endleaf.
WHITE
300
"x5"
EXERCISES
initary Questions
Suppose that F'(x) = f(x) and F(0)=3, F(2) = 7.
What is the area under y =
f(x) over [0,2] if f(x) ≥ 0?
What is the graphical interpretation of F(2) F(0) if f(x) takes on
positive and negative values?
Suppose that f is a negative function with antiderivative F such that
7 and F(3)=4. What is the area (a positive number) between the
is and the graph of ƒ over [1,3]?
ercises
Exercises 1-4, sketch the region under the graph of the function and
ind its area using FTC I
- [0,1]
1 = [1,2]
3.
Are the following statements true or false? Explain.
(a)
FTC I is valid only for positive functions.
(b) To use FTC I, you have to choose the right antiderivative.
(c) If you cannot find an antiderivative of f, then the definite integral
does not exist.
4. Evaluate ef f'(x)dx, where ƒ is differentiable and f(2) = f(9)=4.
7.
(4x-9x²) dx
8.
u² du
2. f(x)=2x-x², [0,2]
9.
(12x³ +3x²-4x)dx
10.
(10x+3x5) dx
4. f(x)=cosx, [0,4]
11
21³-61³) dr
12.
6.
2
2dx
13.
√ydy
Exercises 5-40, evaluate the integral using FTC 1.
5.
Idx
14.
L
•
(5u4
x4/3 dx
en
th
a
REV6](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb6a0ed01-dc7e-4fee-9bdd-27c695376c3b%2F4b2b4729-bfd7-4555-85ca-77055b8e2f5a%2Fj8ssqh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3
where is an antiderivative of f.
Two-step approach for using FTC I to evaluate the definite integral
Compute
- Evaluate
f(x)dx = F(x) + C.
f(x) dx = F(x) = F(b) - F(a).
b
f(x)dx:
Antiderivative formulas are helpful for evaluating definite integrals. See the summary
in Section 5.3 and the table of integrals in this text's endleaf.
WHITE
300
"x5"
EXERCISES
initary Questions
Suppose that F'(x) = f(x) and F(0)=3, F(2) = 7.
What is the area under y =
f(x) over [0,2] if f(x) ≥ 0?
What is the graphical interpretation of F(2) F(0) if f(x) takes on
positive and negative values?
Suppose that f is a negative function with antiderivative F such that
7 and F(3)=4. What is the area (a positive number) between the
is and the graph of ƒ over [1,3]?
ercises
Exercises 1-4, sketch the region under the graph of the function and
ind its area using FTC I
- [0,1]
1 = [1,2]
3.
Are the following statements true or false? Explain.
(a)
FTC I is valid only for positive functions.
(b) To use FTC I, you have to choose the right antiderivative.
(c) If you cannot find an antiderivative of f, then the definite integral
does not exist.
4. Evaluate ef f'(x)dx, where ƒ is differentiable and f(2) = f(9)=4.
7.
(4x-9x²) dx
8.
u² du
2. f(x)=2x-x², [0,2]
9.
(12x³ +3x²-4x)dx
10.
(10x+3x5) dx
4. f(x)=cosx, [0,4]
11
21³-61³) dr
12.
6.
2
2dx
13.
√ydy
Exercises 5-40, evaluate the integral using FTC 1.
5.
Idx
14.
L
•
(5u4
x4/3 dx
en
th
a
REV6
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