1. If f(x) dx = 3, evaluate [[1 + 21(x)] dx using the properties of interga 2. If f(x) dx = -2 and if f(x) dx = 1, evaluate S[x-21(x)] dx using the 0 properties of integral. 3. If ff(x) dx = 5 and f(x) dx = -2, evaluate [ײ + 2-3 f(x)]dx using the properties of integral. 4. If Out If ff(x) dx = 5 and if g(x) dx = -3, evaluate [f(x) + 2 g(x)]dx -1 using the properties of integral.
1. If f(x) dx = 3, evaluate [[1 + 21(x)] dx using the properties of interga 2. If f(x) dx = -2 and if f(x) dx = 1, evaluate S[x-21(x)] dx using the 0 properties of integral. 3. If ff(x) dx = 5 and f(x) dx = -2, evaluate [ײ + 2-3 f(x)]dx using the properties of integral. 4. If Out If ff(x) dx = 5 and if g(x) dx = -3, evaluate [f(x) + 2 g(x)]dx -1 using the properties of integral.
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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Question
58. answer 1 and 4 only, do like this example way
![58 DEFINITE INTEGRALS
TUTORIAL 58
If fr(x) dx
x) dx = 3, evaluate [1 + 2 f(x)] dx using the properties of integral
2. If f(x) dx = = -2 and if f(x) dx = 1, evaluate
S[x-2f(x)]dx
dx using the
0
properties of integral.
3. If f(x) dx = 5 and f(x) dx = -2, evaluate √ [x² + 2-3 f(x)]dx
-1
using the properties of integral.
If f(x) dx = 5 and if g(x) dx = -3, evaluate [f(x) + 2g(x)]*x
using the properties of integral.
If f(x) dx
f(x) dx = 2 and if g(x) dx = 10, evaluate [3 f(x) - g(x)]dx
using the properties of integral.
1
6. If Sf(x) dx = 2 and if Sg (x) dx = -3, evaluate [f(x) - 2g (x) - 4x²]
0
7.
Given f(x) dx = 10, $f(x) dx = 7₁ g(x) dx = 5.
7.
Evaluate Sf(x) dx - S(f(x) - 2 g(x)) dx.
= -1.
2
8. Given g(x) dx = 3, g(x) dx = 7 and
0
0
€ 601 dy
5.
Sf(x) dx](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe78b7236-539d-4269-b9fb-79b7cb15e732%2F37520f80-6716-4c21-8699-2f0872a44a70%2Fee0pvtt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:58 DEFINITE INTEGRALS
TUTORIAL 58
If fr(x) dx
x) dx = 3, evaluate [1 + 2 f(x)] dx using the properties of integral
2. If f(x) dx = = -2 and if f(x) dx = 1, evaluate
S[x-2f(x)]dx
dx using the
0
properties of integral.
3. If f(x) dx = 5 and f(x) dx = -2, evaluate √ [x² + 2-3 f(x)]dx
-1
using the properties of integral.
If f(x) dx = 5 and if g(x) dx = -3, evaluate [f(x) + 2g(x)]*x
using the properties of integral.
If f(x) dx
f(x) dx = 2 and if g(x) dx = 10, evaluate [3 f(x) - g(x)]dx
using the properties of integral.
1
6. If Sf(x) dx = 2 and if Sg (x) dx = -3, evaluate [f(x) - 2g (x) - 4x²]
0
7.
Given f(x) dx = 10, $f(x) dx = 7₁ g(x) dx = 5.
7.
Evaluate Sf(x) dx - S(f(x) - 2 g(x)) dx.
= -1.
2
8. Given g(x) dx = 3, g(x) dx = 7 and
0
0
€ 601 dy
5.
Sf(x) dx
![Given •Sf(x) dx = = -2 and 1(x) dx = 1, find
f(x) dx
S[31(x) + x1dx
$f(x) dx
Sf(x) dx +
-/1(x) dx + 1
0
-(-2) + 1
3
b)
dx
$131(x) + x16x=3/1(x) dx + xdx
v2
5
3 (1) + []X=6
=
- 3+25
1
=
152
Example 3: If f(x) dx =
= -5 and
f(x) dx
-1.
2
S[f(x) = kx] dx = 7, using the properties of integral.
-1
Solution:
[f(x) - kx]dx
7
f(x) dx - kĵx dx = 7
-1
Sf(x) dx + f(x) dx - k[]X=4
= 7
-1
- 5 + 3 k (8-2) = 7
15k = 9
2
k =
b)
Solution:
a)
=
227
f(x) dx
= 3, find the value of k if
6/5
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe78b7236-539d-4269-b9fb-79b7cb15e732%2F37520f80-6716-4c21-8699-2f0872a44a70%2Fi9l2y8f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given •Sf(x) dx = = -2 and 1(x) dx = 1, find
f(x) dx
S[31(x) + x1dx
$f(x) dx
Sf(x) dx +
-/1(x) dx + 1
0
-(-2) + 1
3
b)
dx
$131(x) + x16x=3/1(x) dx + xdx
v2
5
3 (1) + []X=6
=
- 3+25
1
=
152
Example 3: If f(x) dx =
= -5 and
f(x) dx
-1.
2
S[f(x) = kx] dx = 7, using the properties of integral.
-1
Solution:
[f(x) - kx]dx
7
f(x) dx - kĵx dx = 7
-1
Sf(x) dx + f(x) dx - k[]X=4
= 7
-1
- 5 + 3 k (8-2) = 7
15k = 9
2
k =
b)
Solution:
a)
=
227
f(x) dx
= 3, find the value of k if
6/5
1
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