Problem 1E: Let S be the boundary surface of the box enclosed by the planes x = 0, x = 2, y = 0, y = 4, z = 0,... Problem 2E: A surface S consists of the cylinderx2+ y2=1, 1 z 1, together with its top and bottom disks.... Problem 3E Problem 4E: Suppose that f(x,y,z)=g(x2+y2+z2), where g is a function of one variable such thatg(2) =5. Evaluate... Problem 5E: Evaluate the surface integral. 5. s (x + y + z) dS, S is the parallelogram with parametric... Problem 6E: Evaluate the surface integral. 6. s xyz dS, Sis the cone with parametric equationsx = ucosv, y = u... Problem 7E: Evaluate the surface integral. 7. s y dS,Sis the helicoid with vector equation r(u,v) = ucosv,... Problem 8E: Evaluate the surface integral. 8.s (x2+ y2)dS, Sis the surface with vector equation r(u,v)=2uv, u2... Problem 9E: Evaluate the surface integral. 9. s x2yz dS, Sis the part of the planez = 1 + 2x + 3ythat lies above... Problem 10E: Evaluate the surface integral. 10. s xz dS, S is the part of the plane 2x + 2y + z = 4 that lies in... Problem 11E: Evaluate the surface integral. 11. s x dS, S is the triangular region with vertices (1, 0, 0), (0,... Problem 12E: Evaluate the surface integral. 12. s y dS, S is the surface z=23(x3/2+y3/2),0x1,0y1 Problem 13E: Evaluate the surface integral. Sx2z2dS, S is the part of the cone z2 = x2 + y2 that lies between the... Problem 14E: Evaluate the surface integral. SzdS, S is the surface x=y+2z2,0y1,0z1 Problem 15E: Evaluate the surface integral. 15. SydS, S is the part of the paraboloid y = x2 + z2 that lies... Problem 16E: Evaluate the surface integral. 16. Sy2dS, S is the part of the sphere x2+y2+z2=4 that lies inside... Problem 17E: Evaluate the surface integral. 17. s (x2z + y2z)dS, S is the hemisphere x2 + y2 + z2 = 4, z 0 Problem 19E: Evaluate the surface integral. 19. S(z+x2y)dS, S is the part of the cylinder y2+z2=1 that lies... Problem 18E: Evaluate the surface integral. 19. s xz dS, S is the boundary of the region enclosed by the cylinder... Problem 20E: Evaluate the surface integral. 20. s (x2 + y2 + z2) dS, S is the part of the cylinder x2 + y2 = 9... Problem 21E: Evaluate the surface integral s F dS for the given vector field F and the oriented surface S. In... Problem 22E: Evaluate the surface integral s F dS for the given vector field F and the oriented surface S. In... Problem 23E: Evaluate the surface integral s F dS for the given vector field F and the oriented surface S. In... Problem 24E: Evaluate the surface integral s F dS for the given vector field F and the oriented surface S. In... Problem 25E: Evaluate the surface integral SFdS for the given vector field F and the oriented surface S. In other... Problem 26E: Evaluate the surface integral SFdS for the given vector field F and the oriented surface S. In other... Problem 27E: Evaluate the surface integral sFdS for the given vector field F and the oriented surface S. In other... Problem 28E: Evaluate the surface integral SFdS for the given vector field F and the oriented surface S. In other... Problem 29E: Evaluate the surface integral sFdS for the given vector field F and the oriented surface S. In other... Problem 31E: Evaluate the surface integral SFdS for the given vector field F and the oriented surface S. In other... Problem 30E: Evaluate the surface integral SFdS for the given vector field F and the oriented surface S. In other... Problem 32E: Evaluate the surface integral SFdS for the given vector field F and the oriented surface S. In other... Problem 33E: Find the value of Sx2y2z2dS correct to four decimal places, where S is the part of the paraboloid... Problem 35E: Find a formula for s F dS similar to Formula 10 for the case where S is given by y = h(x, z) and n... Problem 36E: Find a formula for s F dS similar to Formula 10 for the case where S is given by x = k(yy z) and n... Problem 37E: Find the center of mass of the hemisphere x2 + y2 + z2 = a2, z 0, if it has constant density. Problem 38E: Find the mass of a thin funnel in the shape of a cone z=x2+y2, 1 z 4, if its density function is... Problem 39E: (a) Give an integral expression for the moment of inertia Iz about the z-axis of a thin sheet in the... Problem 40E: Let S be the part of the sphere x2 + y2 + z2 = 25 that lies above the plane z = 4. If S has constant... Problem 41E Problem 42E Problem 43E: Use Gausss Law to find the charge contained in the solid hemisphere x2 + y2 + z2 a2, z 0, if the... Problem 44E: Use Gausss Law to find the charge enclosed by the cube with vertices (1, 1, 1) if the electric field... Problem 45E: The temperature at the point (x, y, z) in a substance with conductivity K = 6.5 is u(x, y, z) = 2y2... Problem 46E Problem 47E: Let F be an inverse square field, that is, |F(r) = cr/|r|3 for some constant c, where r = x i + y j... format_list_bulleted