S 4) A block is pulled by a force F through a distance L as shown...

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S 4) A block is pulled by a force F through a distance L as shown in the figure. X (cont'd. on back) The angle between the force and the direction of movement is 0. If both the force and the angle vary with position, the work done by the force is W = F(x) cos[6(x)] dx If F(x) = 10x (Newtons), 0(x) = 0.5 - 2x (radians) and L = 0.5 m, calculate W a) Using the composite trapezoid rule with 2 subintervals (3 points). b) Using Simpson's rule. c) Using multiple applications of the midpoint method with 3 subintervals (3 points). d) Using the 4-segment, 3-point Newton-Cotes open-type formula. e) Using the 3-point Gauss-Legendre formula. S 4) A block is pulled by a force F through a distance L as shown in the figure. X (cont'd. on back) The angle between the force and the direction of movement is 0. If both the force and the angle vary with position, the work done by the force is W = F(x) cos[6(x)] dx If F(x) = 10x (Newtons), 0(x) = 0.5 - 2x (radians) and L = 0.5 m, calculate W a) Using the composite trapezoid rule with 2 subintervals (3 points). b) Using Simpson's rule. c) Using multiple applications of the midpoint method with 3 subintervals (3 points). d) Using the 4-segment, 3-point Newton-Cotes open-type formula. e) Using the 3-point Gauss-Legendre formula.