Let $ S $ be the part of the plane $ x + y + z = 2 $ in the first octant oriented up, and let \[\vec{F}(x, y, z) = \langle x + y, x - y, 2z \rangle.\]If we change the surface integral $\iint_S \vec{F} \cdot d\vec{S}$ into iterated integrals, we get:- $ \bigcirc \ 2 \int_0^2 \int_0^{2-x} (x + z) \, dy \, dx $- $ \bigcirc \ \int_0^2 \int_0^2 (4 - 2y) \, dy \, dx $- $ \bigcirc \ \sqrt{3} \int_0^2 \int_0^{2-x} (4 - 2y) \, dy \, dx $- $ \bigcirc \ \int_0^2 \int_0^{2-x} (4 - 2y) \, dy \, dx $

The equation of the plane is: x+y+z=2z=2-x-y Formula: The surface integral over the graph of…

Let S be the part of the plane x + y+ z = 2 in the first octant oriented up, and let F(x, y, z) = (x + Y, x – y, 2z). If we change the surface integral (f. F · dS into iterated integrals, we get: 2-r 2 * (x + z)dydx o f S (4 – 2y)dydx O 13 *(4 – 2y)dydx 2-x OS S*(4 – 2y)dydx 2-x

Let S be the part of the plane x + y+ z = 2 in the first octant oriented up, and let F(x, y, z) = (x + Y, x – y, 2z). If we change the surface integral (f. F · dS into iterated integrals, we get: 2-r 2 * (x + z)dydx o f S (4 – 2y)dydx O 13 (4 – 2y)dydx 2-x OS S(4 – 2y)dydx 2-x

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let $ S $ be the part of the plane $ x + y + z = 2 $ in the first octant oriented up, and let

\[
\vec{F}(x, y, z) = \langle x + y, x - y, 2z \rangle.
\]

If we change the surface integral $\iint_S \vec{F} \cdot d\vec{S}$ into iterated integrals, we get:

- $ \bigcirc \ 2 \int_0^2 \int_0^{2-x} (x + z) \, dy \, dx $

- $ \bigcirc \ \int_0^2 \int_0^2 (4 - 2y) \, dy \, dx $

- $ \bigcirc \ \sqrt{3} \int_0^2 \int_0^{2-x} (4 - 2y) \, dy \, dx $

- $ \bigcirc \ \int_0^2 \int_0^{2-x} (4 - 2y) \, dy \, dx $

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