Calculate the vectors A and C curves given below with aA dl
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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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
Please solve only (a) and (b).
![4. Calculate the vectors A and C curves given below with CA dl
Note: For closed curves, unless the direction is specified separately, take
the counterclockwise direction of rotation. In other integrals, you can
arbitrarily choose the starting and ending points of the integral.
(a) A = xēn + yēy, C : {y = x, z = 0, x E (0, 1)}
(b) A = yẽ, – xẽ,y, C : {x² + y? = 1, z = 0}
(c) Ã = xẽ, + yẽ,, C : {x² + y² = 1, z = 0}
(d) Ā =
C : {y =
x, z = 0, x E (0, 00)}
x² + y²'
(e) Ā
Ex + Cy C:{y = 0, z = 0, x E (0, 0)}
x² + y?'
(f) Ã
C: {x = 0, z = 0, y E (0, 0)}
x² + y?'
-yē, + xēy
x2 + y?
C : {x² + y? = 1, z = 1}
(g) Ā =
||](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F028cc30c-0666-4843-a02b-c768278bfe64%2F13071512-28ed-4398-b7af-981c47727196%2F8wq40s_processed.png&w=3840&q=75)
Transcribed Image Text:4. Calculate the vectors A and C curves given below with CA dl
Note: For closed curves, unless the direction is specified separately, take
the counterclockwise direction of rotation. In other integrals, you can
arbitrarily choose the starting and ending points of the integral.
(a) A = xēn + yēy, C : {y = x, z = 0, x E (0, 1)}
(b) A = yẽ, – xẽ,y, C : {x² + y? = 1, z = 0}
(c) Ã = xẽ, + yẽ,, C : {x² + y² = 1, z = 0}
(d) Ā =
C : {y =
x, z = 0, x E (0, 00)}
x² + y²'
(e) Ā
Ex + Cy C:{y = 0, z = 0, x E (0, 0)}
x² + y?'
(f) Ã
C: {x = 0, z = 0, y E (0, 0)}
x² + y?'
-yē, + xēy
x2 + y?
C : {x² + y? = 1, z = 1}
(g) Ā =
||
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