If C is the line segment that first connects point 2 to point i, and then the spring piece that connects point i to point -1 on the unit circle: Integral=?
If C is the line segment that first connects point 2 to point i, and then the spring piece that connects point i to point -1 on the unit circle: Integral=?
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
If C is the line segment that first connects point 2 to point i, and then the spring piece that connects point i to point -1 on the unit circle:
Expert Solution
Step 1
Consider two regions C1 and C2 then these can be defined as follows,
Thus, C=C1UC2
The conjugate of C1=z(t) is (2-2t)-it and the conjugate of C2 is e-it.
Differentiate the C1 with respect to t.
First, obtain the value of the integral of C1 and substitute the value of dz.
Differentiate the C2 with respect to t.
Obtain the value of the integral of C2 and substitute the value of dz.
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