(4, w/8) 1. (y cos xy dx + x cos xy dy) (0,0) (0,5) 2. e2* dx + ye2 dy) (5,0) (1,1) 3. 2(x dx +y dy) (-1,-1) (6, m) 4. | (cos? y dx 2x cos y sin y dy) (2,0) (0,1,2) 5. (z e** dx + dy + xe** dz) (2,3,0) (1,1,0) 6. 2-2: (x dx + y dy - dz) (0,0,0) (780)
(4, w/8) 1. (y cos xy dx + x cos xy dy) (0,0) (0,5) 2. e2* dx + ye2 dy) (5,0) (1,1) 3. 2(x dx +y dy) (-1,-1) (6, m) 4. | (cos? y dx 2x cos y sin y dy) (2,0) (0,1,2) 5. (z e** dx + dy + xe** dz) (2,3,0) (1,1,0) 6. 2-2: (x dx + y dy - dz) (0,0,0) (780)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![PROBLEM SET 10.2
1-8 PATH-INDEPENDENT INTEGRALS
Show that the form under the integral sign is exact in the
plane (Probs. 1-4) or in space (Probs. 5-8) and evaluate
the integral. (Show the details of your work.)
(4, m/8)
1.
(y cos xy dx + x cos xy dy)
(0,0)
2.
(0,5)
(ye2* dx + ye²* dy)
(5,0)
(1,1)
3.
(-1,-1)
2-
(r dx + y dy)
(6,7)
| (cos? y dx - 2x cos y sin y dy)
4.
(2.0)
(0,1,2)
5.
(z e** dx + dy + xe* dz)
(2,3.0)
(1.1,0)
6.
|+y?-2: (x dx + y dy - dz)
(0,0,0)
(7.8,0)
7.
(2ry dx + x dy + sinh z dz)
1.0,0)
(4,4,0)
8.
(2,0,1)
z3) dx + 3x2y2 dy - 3x222 dz]
9. Show that in Example 4 of the text we have
F = grad (arctan (y/x)). Give examples of domains in
which the integral is path independent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F056500a3-b512-40c7-84f8-2e15b6a39543%2F51ddff1d-f39e-44b7-98a6-210678177122%2Fx5td9to_processed.jpeg&w=3840&q=75)
Transcribed Image Text:PROBLEM SET 10.2
1-8 PATH-INDEPENDENT INTEGRALS
Show that the form under the integral sign is exact in the
plane (Probs. 1-4) or in space (Probs. 5-8) and evaluate
the integral. (Show the details of your work.)
(4, m/8)
1.
(y cos xy dx + x cos xy dy)
(0,0)
2.
(0,5)
(ye2* dx + ye²* dy)
(5,0)
(1,1)
3.
(-1,-1)
2-
(r dx + y dy)
(6,7)
| (cos? y dx - 2x cos y sin y dy)
4.
(2.0)
(0,1,2)
5.
(z e** dx + dy + xe* dz)
(2,3.0)
(1.1,0)
6.
|+y?-2: (x dx + y dy - dz)
(0,0,0)
(7.8,0)
7.
(2ry dx + x dy + sinh z dz)
1.0,0)
(4,4,0)
8.
(2,0,1)
z3) dx + 3x2y2 dy - 3x222 dz]
9. Show that in Example 4 of the text we have
F = grad (arctan (y/x)). Give examples of domains in
which the integral is path independent.
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