Question

Compute the surface integral of the vector field F(x, y, z) = (x, y, z) over the surface $T = {(x, y, z) in mathbb{R}^3 : x, y, z ge 0, x + y + z = 1}$ oriented by the upward pointing unit normal.

          Compute the surface integral of the vector field F(x, y, z) = (x, y, z) over the surface

$T = {(x, y, z) in mathbb{R}^3 : x, y, z ge 0, x + y + z = 1}$

oriented by the upward pointing unit normal.

Added by James A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Zack A

10/06/2024

Step 1

We can do this by letting x = 1 and solving for y and z in the equation I + y + 2 = 1. This gives us y = -1 and z = 0. So, a parameterization of T is: r(u,v) = <1, u, 2+v-2u>, where -1 ≤ u ≤ 8 and 0 ≤ v ≤ 20-u. Show more…

Show all steps

Thanks for your feedback!

Compute the surface integral of the vector field F(x,y,z) = (x,y,z) over the surface T = {(x,y,z) ∈ ℐ³ : x,y,z ≥ 0, x+y+z = 1} oriented by the upward pointing unit normal.