#31
25. A cone will 7s0 Surface Integrals using a parametric description Evaluate the suface inegralsK.y)ds using a parametric description af the supface 26. The cap of the sphere +y'+- 4, for f( x, y, z) = 'x 2 + y 2, where S is the hemisphere 27, 3 ++-36, for z 0 28ã /(x, y, z) = y, where S is the cylinder x2 + yi-9, 0 29, f(x, y, z) = x, where s is the cylinder x2 + z 1,0 ere in the 30, np. e,e) = cos Ï, where s is the part of the unit sp first octant 31-34. Surfuce area using an explicit description Find the area of the following surfaces using an explicit description of the surface. 31· The cone z2 = 4(x2 + y2), for 0 z 32. The paraboloid z = 2(x2 + y2), for 0 2.0 4 z s 8 33. The trough z x2, for-2 x ys 4 34. The part of the hyperbolic paraboloid z = x2-y2 above the s 35-38. Surface integrals using an explicit description Evaluate the surface integral JIsfx, y, z) ds using an explicit representation of t urface. 5, rx, y, z) = xy; S is the plane z = 2-x-y in the first oct f(r, y, z) = x2 + y2; S is the paraboloid z = x2 + y2, for 0 szs4. f(x, y, z) origin with radius 5, for z 25-x2-y: S is the hemisphere centered at 2 0 rx, y, z) = e: S is the ni