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3). Let be the part of surface 2 = 2.ry that lies inside the cylinder 2?...
Let E be the solid that lies inside the cylinder x^2 + y^2 = 1,
above the xy-plane, and below the plane z = 1 + x. Let S be the
surface that encloses E. Note that S consists of three sides: S1 is
given by the cylinder x^2 + y^2 = 1, the bottom S2 is the disk x^2
+ y^2 ≤ 1 in the plane z = 0, and the top S3 is part of the plane z...
6. Let S be the part of the cylinder x2 + y2 = 4 that lies between the two planes z = 2 – X and z = –2 – x. Note that S meets either plane on an ellipse, equipped with the outward normal of the cylinder. Sketch S and find the flux of the vector field F = (2x, y, x) through S.
Consider the vector field F(x, y, z) -(z,2x, 3y) and the surface z- /9 - x2 -y2 (an upper hemisphere of radius 3). (a) Compute the flux of the curl of F across the surface (with upward pointing unit normal vector N). That is, compute actually do the surface integral here. V x F dS. Note: I want you to b) Use Stokes' theorem to compute the integral from part (a) as a circulation integral (c) Use Green's theorem (ie...
2. Evaluate the surface integral (cos(zz),3ev,-e y) and S is the part of the sphere z2+-2)2 8 where F(x, y,z) that lies above the ry-plane, oriented by outward normal.
2. Evaluate the surface integral (cos(zz),3ev,-e y) and S is the part of the sphere z2+-2)2 8 where F(x, y,z) that lies above the ry-plane, oriented by outward normal.
(1 point) Let S be the part of the plane z 4 y which lies in the first octant, oriented upward. Evaluate the flux integral of the vector field F 2i + j + 3k across the surface S (with N being the unit upward vector normal to the plane). B.I 48 C. I 72 E. 1 24
(1 point) Let S be the part of the plane z 4 y which lies in the first octant, oriented upward. Evaluate...
Il 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, y, z) = y) - zk, S consists of the paraboloid y = x2 + 22,0 Sys1, and the disk x2 + z2 s 1, y = 1. Evaluate the surface integral F.ds for the given vector field F and the oriented surface S....
1. Let F(x,y,z) =< 32, 5x, – 2y >. Use Stokes's Theorem to evaluate the integral Scurl F.ds, where S is the part of the paraboloid z = x² + y2 that lies below the plane z = 4 with upward- pointing normal vector.
Compute the following surface areas: (a) the surface area of that part of the plane z = Ar + By C which lies inside the y2 elliptical cylinder 1. (b) the surface area of that part of the cylinder r2 +y2 the sphere 2 y 2 0 which lies inside 2ar 4a2. (Notice the symmetry)
please just the final answer for both
Evaluate the surface Integral || 5. ds for the given vector fleld 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, y, z) = yi - xj + Szk, S is the hemisphere x2 + y2 + y2 = 4, 220, oriented downward 26.677 X Evaluate the surface integral llo F.ds for the given vector field F...
Problem 17.(30 points) Let S be the part of the graph of z -2 +zy - 2 which lies inside of the cylinder z2 +v-1. Find the surface integral JJs v1+5z +5y* ds.
Problem 17.(30 points) Let S be the part of the graph of z -2 +zy - 2 which lies inside of the cylinder z2 +v-1. Find the surface integral JJs v1+5z +5y* ds.