Flux Problem: Calculate from (4,6) to (2,6)

[Chadlee88]

Homework Statement

Calculate the flux:
line from (4,6) to (2,6)

using formula: integral v.n dS where v = -yi+xj

n = j
Parametrising:
x = t:
y = 6
Therefore r(t) = ti+6j
r'(t) = i
dS = |r't|dt =>dS = dt

v.n = (-6i+tj) . (j) => t

(As line is going from right to left (4,6) to (2,6))
Lower bound of integration = 4:
Upper bound of integration = 2:

Evaluation:

integral of t dt = t^2/2

therefore Answer is [2^2/2] - [4^2/2] = 2-8 = -6.

The correct answer I'm given is 6 but i don't know where I've gone wrong. could someone please tell me

Homework Equations

The Attempt at a Solution

 

[Pseudo Statistic]

Depends on the direction of flux the question is interested in-- by taking n =j, you assumed they were interested in the flux in the +y direction-- maybe the question wanted the flux in the -y direction? (Which would give you the negative of the n you obtained)