Number 1 o find anti-derivatives of vector fieldso compute path integrals via the FTC1. Let F(x, y) = (y). Is there a scalar-valued function f(x, y) suchthat F Vƒ? If not say why not, and if so find f.2. Let F(x, y) = (sin(e)-v). Is there a scalar-valued function f(x, y) suchthat F = Vƒ? If not say why not, and if so find f.sin r+sin yy). Is there a scalar-valued function g(x, y)such that F= Vƒ? If not explain why, and if so find f.3. Let F(x, y)=

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Answered: 1. Let F(x, y) = (279). Is there a…

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

Number 1

o find anti-derivatives of vector fields
o compute path integrals via the FTC
1. Let F(x, y) = (y). Is there a scalar-valued function f(x, y) such
that F Vƒ? If not say why not, and if so find f.
2. Let F(x, y) = (sin(e)-v). Is there a scalar-valued function f(x, y) such
that F = Vƒ? If not say why not, and if so find f.
sin r+sin y
y). Is there a scalar-valued function g(x, y)
such that F= Vƒ? If not explain why, and if so find f.
3. Let F(x, y)
=

Expert Solution

Step 1: To check F is coservative or not:

$F with rightwards arrow on top left parenthesis x comma y right parenthesis equals open parentheses table row cell x minus y end cell row x end table close parentheses equals open parentheses table row cell M left parenthesis x comma y right parenthesis end cell row cell N left parenthesis x comma y right parenthesis end cell end table close parentheses H e r e comma space fraction numerator partial differential M over denominator partial differential y end fraction equals negative 1 space a n d space fraction numerator partial differential N over denominator partial differential x end fraction equals 1 T h e r e f o r e space fraction numerator partial differential M over denominator partial differential y end fraction not equal to fraction numerator partial differential N over denominator partial differential x end fraction. H e n c e space F with rightwards arrow on top left parenthesis x comma y right parenthesis space i s space n o t space c o n s e r v a t i v e.$