Problem 1: Length of a curve given by the equation y = f(x) between points a and b can be derived as: b L-√√√1+(f(x))² dx = a Consider the shape of the Golden Gate Bridge as shown in the figure below. The central span of the bridge 4200 ft long and the tower's height from the roadway is 500 ft. The shape of the main suspension cables can be approximately modeled by the equation: f(x)=C exic -x/C +e 2 for-2100 < x < 2100 ft, where C = 4491. y A y=f(x)- a b y 2100 ft 500 ft By using the given equation for the length of a curve, L, determine the length of the main suspension cables with the following integration methods. A) Using Trapezoidal method, with 8 intervals (on paper, using a calculator, make sure to include details of your calculations). B) Using Gauss quadrature method with 4 quadrature points (on paper, using a calculator, make sure to include details of your calculations). C) Use MATLAB's built-in functions “quad" and "trapz”. Include all lines of code that you write for this part.