s - the first octant portion of zx2 over xa (b) (4 pts) Be sure to sketch the surface. s - the first octant portion of zx2 over xa (b) (4 pts) Be sure to sketch the surface.
-. (15 pts.) Let S is the first-octant portion of the plane 2x + y +z = 4. Evaluate the surface integral SSE (2y2 + 2yz) ds.
Questions Evaluate S 45ydo over the surface S, the first octant of the plane +2y+2z = 4. a) 16 b) 16 3 c) 16 3 d) O-16 8
Use Stokes's Theorem to evaluate F dr. In this case, C is oriented counterclockwise as viewed from above. S: the first-octant portion of x2 + z2 -64 over x2 + y2-64 Use Stokes's Theorem to evaluate F dr. In this case, C is oriented counterclockwise as viewed from above. S: the first-octant portion of x2 + z2 -64 over x2 + y2-64
5. (6) Consider the solid bound in the first octant by the surface 9x2 +4y 36 and the plane 9x+ 4y + 6z 36. a. Sketch the solid. b. Set-up the integral to find the volume of the solid by using a double integral. DO NOT INTEGRATE 5. (6) Consider the solid bound in the first octant by the surface 9x2 +4y 36 and the plane 9x+ 4y + 6z 36. a. Sketch the solid. b. Set-up the integral to...
Let S be the portion of the cylinder y =e* in the first octant that projects parallel to the x-axis onto the rectangle Rg: 1sys3, Oszs1 in the yz-plane (see the accompanying figure). Let n be the unit vector normal to S that points away from the yz-plane. Find the flux of the field F(x.y.z) = - 21-4yj + zk across S in the direction of n. Rya The flux is. (Type an exact answer.)
5. Calculate the surface area of the portion of the sphere x2+y2+12-4 between the planes z-1 and z ะไ 6. Evaluate (xyz) dS, where S is the portion of the plane 2x+2y+z-2 that lies in the first octant. 7. Evaluate F. ds. a) F = yli + xzj-k through the cone z = VF+ア0s z 4 with normal pointing away from the z-axis. b) F-yi+xj+ek where S is the portion of the cylinder+y9, 0szs3, 0s r and O s y...
solve parts b,d and f 2. Compute the integral of f over S where (a) f(ayz)xy+z.S is the region in the first octant with xy+ (b) f(xy.z)xxyz, S is the region defined in 2(a) (c) f(x,y.z) x + y2-xz, s is the region bounded by the x'y plane, the plane z (d) f(x,y,z) 2, and the cylinderx2 y z, s is the region in the first octant bounded by r2 + y2 + 2 4 (e) f(xy,z-2, s is the...
6. Find the area of the portion of the surface x.))4 that lies above the region R-((r, y): O S x 6, 0 Sy 6-x), Round your answer to two decimal places. a. 0.67 b.3.87 c. 30.30 d. 10.64 e. 30.84 # 100-х.-)" in the first 7. Find the area of the surface for the portion of the paraboloid octant. a T401401- b. %(1,001 v 1,001-3) c. (101 TOI-3 60 d. 1,003 1,003-3) 101101-1 8. Use an iterated integral to...
Question 9 8 pts (8) Let S be the solid in the first octant that lies inside the sphere p = 2 and underneath the cone == 33° + 3y". Set up a triple integral in spherical coordinates that represents the volume of S.
Evaluate the surface integralG(x, y, z) ds G(x, y, z) (x2 +y')z; S that portion of the sphere x2 + y2 + z2-16 in the first octant eBook