1 (12pts). Evaluate J (4+ xy)ds, where the curve C is the line segment from (-3,-1) to (1.2). 2 (12pts). Find the work d

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1 12pts Evaluate J 4 Xy Ds Where The Curve C Is The Line Segment From 3 1 To 1 2 2 12pts Find The Work D 1 (35.7 KiB) Viewed 14 times

1 (12pts). Evaluate J (4+ xy)ds, where the curve C is the line segment from (-3,-1) to (1.2). 2 (12pts). Find the work done f F dF by the force F = -4x + 4yj + 4k in moving a particle along F(t) = 3cos(t)ī+3 sin(t)j + 2tk. 0 ≤t≤ 2. 3 (14pts). F = (5 + 4xy)i + (2x² - 3y²)j- (1) Show that F is conservative and then find a function with f(0,0) = 2 such that Vf= F. (2) Use the function fto evaluate F-dr, where the curve C: F(t) = e¹¹ cos(t)i + e¹¹ sin(t)j, 0 ≤ t ≤n. 4 (12pts). Use Green's Theorem to evaluate the line integral along the given positively oriented curve 1 = √ (4y + 7e¹x) dx + (3x² + cos(y²))dy, where the curve C is the circle x² + y² = 4. 5 (12pts). Find the area of the part of the paraboloid z = 2x² + 2y², where 0 ≤ z ≤ 2. 6 (12pts). F = (3z + 5y)i + (3z + 5x)j + (3y + 3x)k. (1) Calculate curlF. (2) Is there a function f such that Vf= F? If yes, find a f. 7 (13pts). Evaluate f (x+y+62)ds, where S is the surface with 7(u, v) = (3 + 6u +4v)i + (u − v)j + (u + v)k,0 ≤u≤ 1,0 ≤ v≤ 2. 8 (13pts). Calculate ff F-ds, where F = yi+xj + 2zk and S is the surface of the paraboloid z = 9-x² - y² that lies above the xy-plane and the upward orientation.