1) Evaluate the following line integrals over the indicated curves. a) [(2xy,x-2y) dr where C: r(t) = sen(t) i - 2 cos(t

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1 Evaluate The Following Line Integrals Over The Indicated Curves A 2xy X 2y Dr Where C R T Sen T I 2 Cos T 1 (44.71 KiB) Viewed 75 times

1) Evaluate the following line integrals over the indicated curves. a) [(2xy,x-2y) dr where C: r(t) = sen(t) i - 2 cos(t) j; con t € [0,7]. Answer. 0.435 b) [(3xy,4x² - 3y) dr where C is the line from (0.3) to (3.9) and then the parabola y = x² de • (3,9) a (5,25). Answer. 1477/2 ((z.x,y) dr dr donde C: r(t) = a cos(t) i + a sen(t) j + tk; con t€ [0,2π]. Answer π(a²+2a) 2) Calculate the work done by each of the following vector fields when moving on the given path, the arc is measured in meters and the force in newtons. a) F(x,y,z) = exi+eYj+e² k; where C is described por r(t) = ti+t²j+t³ k; con t= [0,2]. Answer. We 2 te 4 te8 e 8-3 joules. b) F(x,y,z) = xi+yj + (yz -x) k; C is described by r(t) = 2 ti+t2j+ 4t 3 k. Con te [0,1]. Answer W=2.5 joules. 3) Evaluate the following line integrals: a) [x²y dx - y² x²y dx - y²x dy where C is the circunference x 2 + y2 = 1. Answer - 1/2. b) (x + y) dx + xy dy where C is the closed curve determined by the x-axis, the line x = 2 and the curve 4 y = x 3. Answer -3/7. c) cos(y) dx + cos(x) dy where C is the rectangle with vertices at (0,0),(π/3,0),(π/3,π/4) y (0,π/4). Answer (5-4 √2)π/24 d) [(ex − x²y) dx + 3x²y dy where C is the closed curve determined by y= x², x= y2. Answer 41/70. e) (sen¹ (x) + e²x) dx + (cos² (1) − ³) dy where C is the curve x 4 + y 4 = 16. Answer 0.