1.Find the area below z = x^2y and above the linear path from (1,2) to (6,4) in ?^2.
2.Evaluate ∫c f ⋅ dr, where F(x, y) = 〈3x2, 2x + y〉 and C is the line from (0,2) to (5,1).
3.Evaluate ∫c f ⋅ dr, where F(x, y) = 〈3x^2y^2 ,2x^3y〉 and C is the sequence of segments from (2,3) to (5,1) to (8,4) to (1,5)
4.Evaluate ∫c f ⋅ dr, where F(x, y) = 〈4y, 3x + 2y〉 and C is a circle of radius 6, centered at the origin, traversed in the clockwise direction.
5.Evaluate ∫c f ⋅ dr, where F(x, y) = 〈sin(x^2) + 2y, 2x − √y^2 − 3y + 2〉 and C is a triangle from (0,0) to (5,0) to (1,8) back to (0,0).
6.Find the surface area of the portion of the plane 2x + y + 6z = 12 that lies in the first octant.