(a) Derive the analogs of Formulas (12) and (13) for surfacesof the form x = g(y, z).(b)

Chapter 15, Problem 31

(choose chapter or problem)

(a) Derive the analogs of Formulas (12) and (13) for surfaces of the form \(x = g(y, z)\).

(b) Let \(\sigma\) be the portion of the paraboloid \(x=y^{2}+z^{2}\) for \(x \leq 1\) and \(z \geq 0\) oriented by unit normals with negative x-components. Use the result in part (a) to find the flux of

    \(\mathrm{F}(x, y, z)=y \mathbf{i}-z \mathbf{j}+8 \mathbf{k}\)

across \(\sigma\).

Equation Transcription:

x = y2 + z2 

x ≤ 1

z ≥ 0

σ

Text Transcription:

x = g(y, z)

x = y^2 + z^2

x <= 1

z >= 0

F(x, y, z) = yi-z j + 8k

sigma