Find the area of the following surface using the given explicit description of the surface. The...

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Find the area of the following surface using the given explicit description of the surface. The cone z = (x + y), for 0 z 12 Set up the surface integral for the given function over the given surface S as a double integral over a region R in the xy-plane. S dS= R dA (Type an exact answer, using as needed.) Evaluate the surface integral f(x,y,z) ds using an explicit representation of the surface. S f(x,y,z)=3xy; S is the plane z = 4-x-y in the first octant. Set up the surface integral for the given function f(x,y,z) over the given surface S. Integrate with respect to x first. Use increasing limits of integration. SSO dx dy Sf f(x,y,z) ds = S (Type exact answers.) Evaluate the surface integral S f(x,y,z) ds using an explicit representation of the surface. f(x,y,z) = e; S is the plane z = 18-3x-9y in the first octant. Set up the surface integral for the given function f(x,y,z) over the given surface S. Integrate with respect to x first. Use increasing limits of integration. Ja dx dy SS f(x,y,z) ds = -SS S (Type exact answers.) Find the flux of the vector field F = (0,0,2) across the slanted face of the tetrahedron z = 1-x-y in the first octant. Normal vectors point upward. Set up the integral that gives the flux as a double integral over a region R in the xy-plane. SSF. S Fn ds = R (Type an exact answer.) dA Evaluate the integral using the method of your choice. Assume the normal vectors point outward. SS- (x,0,2) 2 2 nds, where S is the cylinder x + z = a, ly| 2 SS S (x,0,z) n ds = Find the area of the following surface using the given explicit description of the surface. The cone z = (x + y), for 0 z 12 Set up the surface integral for the given function over the given surface S as a double integral over a region R in the xy-plane. S dS= R dA (Type an exact answer, using as needed.) Evaluate the surface integral f(x,y,z) ds using an explicit representation of the surface. S f(x,y,z)=3xy; S is the plane z = 4-x-y in the first octant. Set up the surface integral for the given function f(x,y,z) over the given surface S. Integrate with respect to x first. Use increasing limits of integration. SSO dx dy Sf f(x,y,z) ds = S (Type exact answers.) Evaluate the surface integral S f(x,y,z) ds using an explicit representation of the surface. f(x,y,z) = e; S is the plane z = 18-3x-9y in the first octant. Set up the surface integral for the given function f(x,y,z) over the given surface S. Integrate with respect to x first. Use increasing limits of integration. Ja dx dy SS f(x,y,z) ds = -SS S (Type exact answers.) Find the flux of the vector field F = (0,0,2) across the slanted face of the tetrahedron z = 1-x-y in the first octant. Normal vectors point upward. Set up the integral that gives the flux as a double integral over a region R in the xy-plane. SSF. S Fn ds = R (Type an exact answer.) dA Evaluate the integral using the method of your choice. Assume the normal vectors point outward. SS- (x,0,2) 2 2 nds, where S is the cylinder x + z = a, ly| 2 SS S (x,0,z) n ds =