Question

Find the flux of F across S, $iint_S mathbf{F} cdot mathbf{N} ,dS = iint_R mathbf{F} cdot abla g(x, y) ,dA$ where $z = g(x, y)$ where extbf{N} is the upward unit normal vector to S. $mathbf{F}(x, y, z) = 8zmathbf{i} - 5mathbf{j} + ymathbf{k}$ S: $z = 1 - x - y$, first octant

          Find the flux of F across S,
$iint_S mathbf{F} cdot mathbf{N} ,dS = iint_R mathbf{F} cdot 
abla g(x, y) ,dA$ where $z = g(x, y)$
where 	extbf{N} is the upward unit normal vector to S.
$mathbf{F}(x, y, z) = 8zmathbf{i} - 5mathbf{j} + ymathbf{k}$
S: $z = 1 - x - y$, first octant

Find the flux of F across S,
iintS mathbfF cdot mathbfN ,dS = iintR mathbfF cdot
abla g(x, y) ,dA where z = g(x, y)
where extbfN is the upward unit normal vector to S.
mathbfF(x, y, z) = 8zmathbfi - 5mathbfj + ymathbfk
S: z = 1 - x - y, first octant

Added by Kristina E.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Zack A

09/04/2023

Step 1

Since S is in the first octant and z = 1 - x - y, we can parameterize S as follows: r(u, v) = (u)i + (v)j + (1 - u - v)k, where 0 ≤ u ≤ 1, 0 ≤ v ≤ 1 - u. Now, we need to find the partial derivatives of r with respect to u and v: r_u = ∂r/∂u = (1)i + (0)j - Show more…

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