1. Evaluate the surface integral [[ 3. SS S where S is the portion of the plane x + 2y + z = 2 lying in the first octant. 3-z do,
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- Evaluate the surface integral ffR(x+y)dSwhere σ is the portion of the plane z = 6 − 2x − 3y in the first octantEvaluate the surface integral. S z2 dS, S is the part of the paraboloid x = y2 + z2 given by 0 ≤ x ≤ 4Evaluate the following surface integral. ∫∫S (1 + yz) dS; S is the plane x + y + z = 2 in the first octant.
- Evaluate the surface integral F*n d-sigma where F = 2xi +4zj - 4yk, and S is the part of the sphere x^2 + y^2 + z^2 = 9 in the first octant, with orientation towards the origin.Evaluate the surface integral: x dS, S is the part of the plane 12x + 6y + z = 12 that lies in the first octant.Evaluate the surface integral. S y2 dS S is the part of the sphere x2 + y2 + z2 = 36 that lies inside the cylinder x2 + y2 = 9 and above the xy-plane
- Consider the solid that lies above the square (in the xy-plane) R=[0,2]x[0,2] and below the elliptic paraboloid z=49-x^2-y^2Evaluate the surface integral.∫∫S (x2+y2+z2) dS, S is the part of the cylinder x2+y2 = 9 between the planes z = 0 and z =2, together with its top and bottom disksEvaluate the surface integral. ∫∫s(x2 + y2 + z2) dS, S is the part of the cylinder x2 + y2 = 9 between the planes z = 0 and z = 2, together with its top and bottom disks.