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Let S be the line segment connecting i to 1, oriented either way. Show that 1 1/2 d S dz ≤ 2√2

Let S be the line segment connecting i to 1, oriented either way. Show that 1 1/2 d S dz ≤ 2√2

Advanced Engineering Mathematics
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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Let \( S \) be the line segment connecting \( i \) to 1, oriented either way. Show that \[ \left| \int_S \frac{1}{z^2} \, dz \right| \leq 2\sqrt{2} \]
Transcribed Image Text:Let \( S \) be the line segment connecting \( i \) to 1, oriented either way. Show that \[ \left| \int_S \frac{1}{z^2} \, dz \right| \leq 2\sqrt{2} \]
Expert Solution
Step 1: solving integral using ML inequality .

Sol.    Given that   S is the line segment connecting i to 1.

i.e.,    S={(x,y): x+y=1,  0less or equal thanx,yless or equal than1} .       

DEFINITION: ML inequality;   open vertical bar integral subscript c f open parentheses z close parentheses d z close vertical bar less or equal than M L  ,  where open vertical bar f left parenthesis z right parenthesis close vertical bar less or equal than M and L= length of the curve C.

Advanced Math homework question answer, step 1, image 1 here length of S=L=distance between the points (1,0) and (0,1).

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