Question

Hello
18-02sc-Multivariable Calculus Fall 2010, Session 82: ndS for a Surface z = f(x, y),Problems: Flux Through General Surfaces

I think there is a mistake in the solution given in Problems: Flux Through General Surfaces
\( \left(\int _0^1\int _0^1\{-y,x,0\}.\{ -2 x,-2 y,1\}dydx\right) \)
Wolfram-Alpha:N[Integrate[{-y, x, 0}.{ -2x, -2y, 1},{x, 0, 1} , {y,0, 1} ]]

but the unitary vectors of respectidly x,y,z axis is i,j,k the solution is
\( \left(\int _0^1\int _0^1\{-y,0,x\}.\{-2 x,-2 y,1\}dydx\right)\ \)
Wolfram-Alpha:N[Integrate[{-y, 0, x}.{-2x, -2y, 1},{x, 0, 1} , {y,0, 1} ]]
am i wrong ?

Answer 1

yes, it looks like they meant
\[ \mathbf{F} = -y \mathbf{i} + x \mathbf{j}\]

(or at least, that is what they used when solving)