1b. In the following diagram, the shaded region is enclosed by the graph of f, the graph of g, the z-axis, and the line z ke 2. A Find the value of k and the value of p. B In (P)+8 The area of the shaded region can be written as In (p) +8, where pe Z. x = k Fut X-4+1 = K
1b. In the following diagram, the shaded region is enclosed by the graph of f, the graph of g, the z-axis, and the line z ke 2. A Find the value of k and the value of p. B In (P)+8 The area of the shaded region can be written as In (p) +8, where pe Z. x = k Fut X-4+1 = K
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Can you help with part b, please?
Transcribed Image Text:1b. In the following diagram, the shaded region is enclosed by the graph of f, the graph of g, the z-axis, and the line z k
ke Z
The area of the shaded region can be written as In(p) +8, where p E Z.
Find the value of k and the value of p.
4
X-4
S86)-f(x) = In (p) +8
X-3-
23. x -+-4-2 = In (p) + 8.
41
(RO) (AO)
(40)
5₂ 2²-In (x-4)-2x
1-3
X=X
-x-3= k
In (P)+8
8
= (n/p/xq
x= k
X-4+1=K
X=K = f(x)
₁+1=k
1 +0
(AQ) (MI)
(AL)
(²2-In (ku) - 2k) - 3²2² - \n(5-471-2163)
(MO) (2 - hnck-4)28)+ (8 + In (-1) )= In (P}+8
- (²2-In (-1))
AO
(мо) АОАО)
(x-1)(x-4)=1
*x-x-4x
*x-x-4
K-1-X-4
(2)
![1a. Consider the functions f(x)=+1, for x # 4, and g(x)=x-3 for x ER.
The following diagram shows the graphs of f and g.
y
Find the coordinates of B.
The graphs of f and g intersect at points A and B. The coordinates of A are (3, 0).
+4+1 = x-3
(MI)
B
·B = 5,0 AO..
.X.-4.
X-4
33 min
13
29
35
61
[5 marks]
(4
X-4*X-4
x2 - 4x - 4x + 16
= x-4
0=X²-8x +15 (A1)
.(x-3)(x-5) (M1)
x=3
x=5 A1
14](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2fd56cd7-16d6-42a3-873f-51e9748dabe0%2F910c4cef-e718-43a2-bd62-f875c236f3de%2F8cjme1q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1a. Consider the functions f(x)=+1, for x # 4, and g(x)=x-3 for x ER.
The following diagram shows the graphs of f and g.
y
Find the coordinates of B.
The graphs of f and g intersect at points A and B. The coordinates of A are (3, 0).
+4+1 = x-3
(MI)
B
·B = 5,0 AO..
.X.-4.
X-4
33 min
13
29
35
61
[5 marks]
(4
X-4*X-4
x2 - 4x - 4x + 16
= x-4
0=X²-8x +15 (A1)
.(x-3)(x-5) (M1)
x=3
x=5 A1
14
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Thanks but I am not understanding the
For example A=∫35∫0x-3dydx+∫5k∫01x-4+1dydx =∫35x-3dx+∫5k1x-4+1dx =x22-3x35+lnx-4+x5k =252-15-92+9+lnk-4+k-ln5-4-5 =8+9-15-5+k+lnk-4 =k-3++lnk-4
Is this the integral of 35 integral 0x-3 dydx
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