F(x, y) = M (x, y)i+N(x, y)j is a conservative vector field with potential function f(x, y) Use this information for parts A through C. 11. A) If C is made up of the line segments from the point (0,0) to the point (4,1) and from (4,1 to the point (2,7) and from (2,7) to the point (0,0) then what can be said about M(x, y) dx+ N(x, y) dy ? Explain using theorems or properties of line integrals. В) If C is a simply connected curve from the point (a,b) to the point (c, d) then what can be said about M(x, y) dx+ N(x, y) dy ? Explain using theorems or properties of line C integrals. If C is the parameterized curve r(t) = x1 (t)i+ yj(t)j, astsb and C2 is the parameterized curve r,(s) = x2(s)i+ y2(s)j, c
F(x, y) = M (x, y)i+N(x, y)j is a conservative vector field with potential function f(x, y) Use this information for parts A through C. 11. A) If C is made up of the line segments from the point (0,0) to the point (4,1) and from (4,1 to the point (2,7) and from (2,7) to the point (0,0) then what can be said about M(x, y) dx+ N(x, y) dy ? Explain using theorems or properties of line integrals. В) If C is a simply connected curve from the point (a,b) to the point (c, d) then what can be said about M(x, y) dx+ N(x, y) dy ? Explain using theorems or properties of line C integrals. If C is the parameterized curve r(t) = x1 (t)i+ yj(t)j, astsb and C2 is the parameterized curve r,(s) = x2(s)i+ y2(s)j, c
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
Solve 11. A, B and C. Please solve clearly.
![F(x, y) = M (x, y)i+N(x,y)j is a conservative vector field with potential function f(x, y)
Use this information for parts A through C.
11.
If C is made up of the line segments from the point (0,0) to the point (4,1) and from (4,1)
to the point (2,7) and from (2,7) to the point (0,0) then what can be said about
A)
M(x, y) dx+ N(x, y) dy ? Explain using theorems or properties of line integrals.
B)
If C is a simply connected curve from the point (a,b) to the point (c, d) then what can be
said about
M(x, y) dx+ N(x, y) dy ? Explain using theorems or properties of line
C
integrals.
C) If C¡ is the parameterized curve r¡(t) = x1 (t)i+ y (t) j, a<t<b and C2 is the
parameterized curve r2(s)=x2(s)i+ y2(s)j, c<s<d and (a)=r2(c) and
7(b) = r, (d) then what can be said about
М (х, у) dx + N(х, у) dy and
М (х, у) dx + N(х, у) dy ?
C2
Explain using theorems or properties of line integrals.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f2030df-489c-4c06-8af8-a0bb3fa2ff8f%2Fdda5e588-8172-4003-bb26-c9f214936d10%2F4tig6pd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:F(x, y) = M (x, y)i+N(x,y)j is a conservative vector field with potential function f(x, y)
Use this information for parts A through C.
11.
If C is made up of the line segments from the point (0,0) to the point (4,1) and from (4,1)
to the point (2,7) and from (2,7) to the point (0,0) then what can be said about
A)
M(x, y) dx+ N(x, y) dy ? Explain using theorems or properties of line integrals.
B)
If C is a simply connected curve from the point (a,b) to the point (c, d) then what can be
said about
M(x, y) dx+ N(x, y) dy ? Explain using theorems or properties of line
C
integrals.
C) If C¡ is the parameterized curve r¡(t) = x1 (t)i+ y (t) j, a<t<b and C2 is the
parameterized curve r2(s)=x2(s)i+ y2(s)j, c<s<d and (a)=r2(c) and
7(b) = r, (d) then what can be said about
М (х, у) dx + N(х, у) dy and
М (х, у) dx + N(х, у) dy ?
C2
Explain using theorems or properties of line integrals.
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