Perform the scalar field path integral (1,1/2) ry ds for each of the three paths below. Note: • To enter , you can type 'pi' (be sure to use lowercase) or you can find it under the Symbols or Greek section of the calcpad. Do not enter a numerical approximation. • Remember NOT to evaluate square roots numerically. If you need √2, type it using the calc pad (under operations) or by typing 'sqrt'. • Remember that your tutorial has Hints in it, at the end of each chapter. If you're stuck, they are often quite useful! Path 1: Along the x-axis to (1,0) and then up in the y-direction to (1,1/2). tyds JPath 1 Path 2: Up the y-axis to (0,1/2) and then in the x-direction to (1,1/2). ryds J Path Path 3: Along the curvey = x²/2, starting at (0,0) and ending at (1,1/2). Touth 3² 1 8 ryds = 1 4 5√5 12 + 16 15 X
Perform the scalar field path integral (1,1/2) ry ds for each of the three paths below. Note: • To enter , you can type 'pi' (be sure to use lowercase) or you can find it under the Symbols or Greek section of the calcpad. Do not enter a numerical approximation. • Remember NOT to evaluate square roots numerically. If you need √2, type it using the calc pad (under operations) or by typing 'sqrt'. • Remember that your tutorial has Hints in it, at the end of each chapter. If you're stuck, they are often quite useful! Path 1: Along the x-axis to (1,0) and then up in the y-direction to (1,1/2). tyds JPath 1 Path 2: Up the y-axis to (0,1/2) and then in the x-direction to (1,1/2). ryds J Path Path 3: Along the curvey = x²/2, starting at (0,0) and ending at (1,1/2). Touth 3² 1 8 ryds = 1 4 5√5 12 + 16 15 X
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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Transcribed Image Text:Perform the scalar field path integral
(1,1/2)
xy ds
(0,0)
for each of the three paths below.
Note:
• To enter , you can type 'pi' (be sure to use lowercase) or you can find it under the Symbols or Greek section of the calcpad. Do not enter a numerical approximation.
• Remember NOT to evaluate square roots numerically. If you need √2, type it using the calc pad (under operations) or by typing 'sqrt'.
• Remember that your tutorial has Hints in it, at the end of each chapter. If you're stuck, they are often quite useful!
Path 1: Along the x-axis to (1,0) and then up in the y-direction to (1,1/2).
Spath 1²
ryds
=
Path 2: Up the y-axis to (0,1/2) and then in the x-direction to (1,1/2).
Jeu
ryds
Touth 3²
1
8
=
1
4
Path 3: Along the curve y = x²/2, starting at (0,0) and ending at (1,1/2).
LA**
xyds 5√5 16
12
+
15
X
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