Pls help me this question! Th 1 :F. dS whereF = (x³, y³, 2³) and S is the solid bounded%3Dby the xy plane and the elliptic paraboloid z = 4 – x2 – y?,a) by direct computationb) using Divergence theorem.

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Answered: 1: Evaluate | F- dS whereF = (2³, y°,…

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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Similar questions

Let G be the wedge in the first octant that is cut from the cylindrical solid y2 + z2 ≤ 4 by the planes y=2x and x=0. Evaluate ∫∫G∫ xyz dV .
Use Divergence theorem to find the outward flux of F = 2xz i - 2xy j – z2 k across the boundary of the region cut from the first octant by the plane y + z = 4 and the elliptical cylinder 4x2 + y2 = 16.
Use Divergence theorem to find the ouward flux of F = 2xz i - 3xy j – z2 k across the boundary of the region cut from the first octant by the plane y + z = 4 and the elliptical cylinder 4x2 + y2 = 16
Find the flux F(x,y,z)=2xi+2yj+zk across the part of the paraboloid z=4-x^2-y^2 above the xy-plane with downward orientation.
Use the Divergence Theorem to find the flux of F = xy2i + x2yj + yk outward through the surface of the region enclosed by the cylinder x2 + y2 = 1 and the planes z = 1 and z =-1.
Use the Divergence Theorem to evaluate S F · N dS and find the outward flux of F through the surface of the solid bounded by the graphs of the equations. F(x, y, z) = x2i + xyj + zk Q: solid region bounded by the coordinate planes and the plane 2x + 3y + 4z = 12
Verify Formula (1) in the Divergence Theorem by evaluatingthe surface integral and the triple integral. 1. F(x, y, z) = xi + y j + zk; σ is the surface of the cubebounded by the planes x = 0, x = 1, y = 0, y = 1, z = 0,z = 1.
Let F = (-z2, 2zx, 4y - x2}, and let C be a simple closed curve in the plane x + y + z = 4 that encloses a region of area 16 (Figure 20). Calculate ∮C F • dr, where C is oriented in the counterclockwise direction (when viewed from above the plane).
use divergence theorem to find the outward flux of f =2xzi-3xyj-z^2k across the boundary of the region cut from the first octant by the plane y+z=4 and the elliptical cylinder 4x^2+y^2=16

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1: Evaluate | F- dS whereF = (2³, y°, 2³) and S is the solid bounded %3D by the ry plane and the elliptic paraboloid z = 4 – x² – y², a) by direct computation b) using Divergence theorem.