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1.Find the area below ? = ?^2? and above the linear path from (1,2) to (6,4) in ?^2. 2.Evaluate ? ? ??, where ?(?, ?) = 3?2, 2? + ? and C is the line...

1.Find the area below ? = ?^2? and above the linear path from (1,2) to (6,4) in ?^2.


2.Evaluate ∫? ? ⋅ ??, where ?(?, ?) = 〈3?2, 2? + ?〉 and is the line from (0,2) to (5,1).


3.Evaluate ∫? ? ⋅ ??, where ?(?, ?) = 〈3?^2y^2 ,2?^3?〉 and is the sequence of segments from (2,3) to (5,1) to (8,4) to (1,5)


4.Evaluate ∫? ? ⋅ ??, where ?(?, ?) = 〈4?, 3? + 2?〉 and is a circle of radius 6, centered at the origin, traversed in the clockwise direction.


5.Evaluate ∫? ? ⋅ ??, where ?(?, ?) = 〈sin(?^2) + 2?, 2? − √?^2 − 3? + 2〉 and 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 2? + ? + 6? = 12 that lies in the first octant.

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