below math question Consider F and C below.F(x, y, z) = y2 cos(z) i + 2xy cos(z) j – xy² sin(z) kC: r(t) = t i + sin(t) j + t k,0

Given that : F=y2coszi^+2xycoszj^-xy2sinzk^r(t)=t2i^+sintj^+tk^ PART A To calculate the value of f, F=∇ff=∫Fxdx+∫Fydy+∫Fzdz=xy2coszPART B From the given value we can find the derivative, dr=2ti^+costj^+1k^ The value of the integral will be, ∫∇f.dr=∫F.dr=∫z=01∫y=0-1∫x=02π∇.F dV=∫z=01∫y=0-1∫x=02π∇.∇fdV=0

Answered: Consider F and C below. F(x, y, z) = y2…

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Consider F and C below. F(x, y, z) = y2 cos(z) i + 2xy cos(z) j – xy? sin(z) k C: r(t) = t2 i + sin(t) j + t k, 0stsn (a) Find a function f such that F = Vf. f(x, у, 2) %3D

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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below math question

Consider F and C below.
F(x, y, z) = y2 cos(z) i + 2xy cos(z) j – xy² sin(z) k
C: r(t) = t i + sin(t) j + t k,
0 <t< n
(a) Find a function f such that F = Vf.
f(x, y, z) =
(b) Use part (a) to evaluate
Vf• dr along the given curve C.

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