(7) Let V be the region in R3 enclosed by the surfaces+2 20 and z1. Let S denote the closed surface of V and let n deno...
I'll ask again, Please DON'T use the divergence theroem, I cant do the surface integral. (7) Let V be the region in R3 enclosed by the surfaces ++22,0 and1. Let S denote the closed surface of V and let n denote the outward unit normal. Calculate the flux of the vector field Fx, y, z)(2 - 2)j 22k out of V and verify Gauss' Divergence Theorem holds for this case. That is, calculate the flux directly as a surface integral...
(1) Let P denote the solid bounded by the surface of the hemisphere z -Vl-r-y? and the cone2y2 and let n denote an outwardly directed unit normal vector. Define the vector field F(x, y, z) = yi + zVJ + 21k. (a) Evaluate the surface integral F n dS directly without using Gauss' Divergence Theorem. (b) Evaluate the triple integral Ш div(F) dV directly without using Gauss' Diver- gence Theorem Note: You should obtain the same answer in (a) and...
3) Consider the vector field F-ra where a is a constant vector and let V be the region in R3 bounded by the surfaces r y24,1, z0. Find the outward flux of F i1n across the closed surface S of V 3) Consider the vector field F-ra where a is a constant vector and let V be the region in R3 bounded by the surfaces r y24,1, z0. Find the outward flux of F i1n across the closed surface S...
(1) Let P denote the solid bounded by the surface of the hemisphere zV1--y2 and the cone z-Vx2 + y2 and let n denote an outwardly directed unit normal vector. Define the vector field (a) Evaluate the surface integral F nds directly without using Gauss' Divergence T heorem (b) Evaluate thetriplengral IIdiv(F) dV directly without using Gauss Diver- gence Theorem. confirming the result of Gauss' Divergence Theorem for this particular example. (1) Let P denote the solid bounded by the...
Let P denote the solid bounded by the surface of the hemisphere z -vl--g and the cone z-Vr2 + y2 and let n denote an outwardly directed unit normal vector Define the vector field (a) Evaluate the surface inteFn dS directly without using Gauss' Divergence aP Theorem (b) Evaluate the triple integraldiv(F) dV directly without using Gauss' Diver gence Theorem. Note: You should obtain the same answer in (a) and (b) In this question you are confirming the result of...
Help would be greatly appreciated!! 1. Let S be the surface in R3 parametrized by the vector function ru, v)(,-v, v+ 2u) with domain D-{(u, u) : 0 u 1,0 u 2). This surface is a plane segment shaped like a parallelogram, and its boundary aS (with positive orientation) is made up of four line segments. Compute the line integral fos F -dr where F(z, y, z) = 〈エ2018 + y, 2r, r2-Ins). Hint: use Stokes' theorem to transform this...
(1) Let F denote the inverse square vector field (axr, y, z) F= (Note that ||F 1/r2.) The domain of F is R3\{(0, 0, 0)} where r = the chain rule (a) Verify that Hint: first show that then use (b) Show that div(F 0. (c) Suppose that S is a closed surface in R3 that does not enclose the origin. Show that the flux of F through S is zero. Hint: since the interior of S does not contain...
(1 point) Let F(2, y, z) be a vector field, and let S be a closed surface. Also, let D be the region inside S. Which of the following describe the Divergence Theorem in words? Select all that apply. L A. The outward flux of F(x, y, z) across S equals the triple integral of the divergence of F(2, y, z) on D. IB. The outward flux of F(x, y, z) across S equals the surface integral of the divergence...
Let E-xi vi + 2zk be an electrostatic field. Use Gauss's Law to find the total charge enclosed by the closed surface consisting of the hemisphere- V1-x2 - y2 and its circular base in the xy-plane. Use the Divergence Theorem to evaluate F.N dS and find the outward flux of F through the surface of the solid bounded by the graphs of the equations. Use a computer algebra system to verify your results F(x, y, z) =xyì + 7yj +xzk...
Evaluate the surface integral F·dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, v, z)-xiyj+8 k S is the boundary of the region enclosed by the cylinderx2+2-1 and the planes y-o and xy6 Evaluate the surface integral F·dS for the given vector field F and the oriented surface S. In other words, find the flux of F across...