Answer this mcq question plz 4) The wode af the veeken fleledFOX,Y) = x-Y, *y)X-yX+yと-(x) ER?: 1 3 (x-3)+854,り2?Path one time in an onti elockwise wayAstBIT2.C) 3 T

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Description: Answer this mcq question plz 4) The wode af the veeken fleledFOX,Y) = x-Y, *y)X-yX+yと-(x) ER?: 1 3 (x-3)+854,り2?Path one time in an onti elockwise wayAstBIT2.C) 3 T

Given : vector field F→x, y=x-y2, x+y2 and set D=x, y∈ℝ2 : 1≤x-32+y2≤4 , y≥0 To find : the work of…

Answered: The work af the veeken fieled aleng the…

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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Answer this mcq question plz

4) The wode af the veeken fleled
FOX,Y) = x-Y, *y)
X-y
X+y
と
-(x) ER?: 1 3 (x-3)+854,り2?
Path one time in an onti elockwise way
Ast
BIT
2.
C) 3 T

Expert Solution

Step 1

Given : vector field $\vec{F} (x, y) = <\frac{x - y}{2}, \frac{x + y}{2}>$ and set $D = \{(x, y) \in ℝ^{2} : 1 \leq {(x - 3)}^{2} + y^{2} \leq 4, y \geq 0\}$

To find : the work of the vector field along the edge of the set D and the path is traversed once in an anti-clockwise way

Pre-requisite :

Green's Theorem - Let C be a positively oriented, piecewise smooth, simple, closed curve and let D be the region enclosed by the curve. If P and Q have continuous first order partial derivatives on D, then

$\oint_{C} P d x + Q d y = \iint_{D} (\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}) d A$

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