Problem 1 (25 points): The central span of the Golden Gate bridge is 4200 ft long and the tower's height from the roadway is 500 ft. 500 ft 2100 ft The shape of the main suspension cables can be approximately modeled by the equation f(x)=c( = c (exic + e-xic -1) 2 for-2100 ft < x < 2100 ft and C = 4491 By using the equation L= = 200 √1 + 1/'(x)]² dx -2100 Note that f'(x) = Determine the length (L) of the main suspension cable using the following integration method (a) Three-point Gauss quadrature (b) Four-point Gauss quadrature. п (Number Coefficients C of points) (weights) 2 C₁ = 1 C₁ = 1 3 C₁ 4 -0.5555556 C₁ 0.8888889 C₁ -0.5555556 C₁ Gauss points x xj -0.57735027 x2 = 0.57735027 * - -0.77459667 *2-0 X3 0.77459667 x=-0.86113631 = 0.3478548 C₂ = 0.6521452 C₁ = 0.6521452 C₁ = 0.3478548 X2 x3 -0.33998104 0.33998104 x=0.86113631