1720 Find the flux of the vector field F across in the directionof positive orientation

Chapter 15, Problem 17

(choose chapter or problem)

Find the flux of the vector field $F$ across $\sigma$.

$F\left(x_{1}, y, z\right)=x i+y j+k: \sigma$ is the portion of the paraboloid $r(u, v)=u \cos\ v i+u\ \sin v j+\left(1-u^{2}\right) k$

with $1 \leq u \leq 2,0 \leq v \leq 2 \pi$.

Equation Transcription:

$F$

$F(x,\ y,\ z)\ =\ xi\ +\ y\ j\ +\ k;$ σ

$\ r(u,\ v)\ =\ u\ cos\ vi\ +\ u\ sin\ v\ j\ +\ (1-{u}^{2})k$

1 ≤ u ≤ 2, 0 ≤ v ≤ 2π

Text Transcription:

sigma

F(x, y, z) = xi + y j + k;sigma

r(u, v) = u cos vi + u sin v j + (1 − u^2)k

1 <= u <= 2, 0 <= v <= 2pi

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