Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.2: Remainder And Factor Theorems
Problem 51PS
Related questions
Question
pls help me with question 1 and 4, do like this example
![59 DEF
Given f(x) =
TUTORIAL 59
4- X
1
x ≤ 1
Find k if
X > 1
Skf(x) dx = -1.
[2 f (x) - g (x)] dx if ff(x) dx = -3 and g(x) = -
7
2. Find
1-X 1
Sf(x) dx = -5 and g(x) dx =
x² - 1:
0≤x<3
{
3. Given
0
3x + 2;
3≤x≤5
Using the properties of definite integral, find the value of k that satisfies
0
S[3g (x) - kf(x)] dx = -2.
x² x ≤ 2
{
x > 2
4. Evaluate f(x) dx if f(x) =
0
5. Evaluate f(x) dx if f(x) =
6. Evaluate f(x) dx if f(x):
3x 2
sec²x ; x ≤ 1
1
; x > 1
X
cos 2x ; x < 0
e²x ; x ≥ 0
√x.x20
X, X Σ Ο
r so
MAT 421
3 ≤x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe78b7236-539d-4269-b9fb-79b7cb15e732%2F4ad594d0-44e5-4c52-8310-1ebd45434b74%2Fxu8wctm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:59 DEF
Given f(x) =
TUTORIAL 59
4- X
1
x ≤ 1
Find k if
X > 1
Skf(x) dx = -1.
[2 f (x) - g (x)] dx if ff(x) dx = -3 and g(x) = -
7
2. Find
1-X 1
Sf(x) dx = -5 and g(x) dx =
x² - 1:
0≤x<3
{
3. Given
0
3x + 2;
3≤x≤5
Using the properties of definite integral, find the value of k that satisfies
0
S[3g (x) - kf(x)] dx = -2.
x² x ≤ 2
{
x > 2
4. Evaluate f(x) dx if f(x) =
0
5. Evaluate f(x) dx if f(x) =
6. Evaluate f(x) dx if f(x):
3x 2
sec²x ; x ≤ 1
1
; x > 1
X
cos 2x ; x < 0
e²x ; x ≥ 0
√x.x20
X, X Σ Ο
r so
MAT 421
3 ≤x
![Example 5:
Evaluate
Solution:
f(x) dx if f(x) =
X
f(x) dx = f(x) dx + $1(x) dx
=
(x² + 1) dx +
S z dx
+ x +
c]
+ [Inx +
c] x=²
[ + 1 ] - [ −
− 1] + + In 2 - In 1
3.36
=
DEFINITE INTEGRALS
x² + 1
: x ≤ 1
1
X > 1
Example 6:
Evaluate f(x) dx if f(x) = {
Solution:
=
-1
sec² 3x ; x > 1
e³x
;
x ≤ 1
f(x) dx = f(x) dx +
f(x) dx
-1
Se³x dx + √ sec² 3x dx
-1
1
3x
[*]*** [tan 3x1x=²
=1
+
[ee]+[tan 6-tan 3]
6.53](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe78b7236-539d-4269-b9fb-79b7cb15e732%2F4ad594d0-44e5-4c52-8310-1ebd45434b74%2Fj034hk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Example 5:
Evaluate
Solution:
f(x) dx if f(x) =
X
f(x) dx = f(x) dx + $1(x) dx
=
(x² + 1) dx +
S z dx
+ x +
c]
+ [Inx +
c] x=²
[ + 1 ] - [ −
− 1] + + In 2 - In 1
3.36
=
DEFINITE INTEGRALS
x² + 1
: x ≤ 1
1
X > 1
Example 6:
Evaluate f(x) dx if f(x) = {
Solution:
=
-1
sec² 3x ; x > 1
e³x
;
x ≤ 1
f(x) dx = f(x) dx +
f(x) dx
-1
Se³x dx + √ sec² 3x dx
-1
1
3x
[*]*** [tan 3x1x=²
=1
+
[ee]+[tan 6-tan 3]
6.53
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