The trapezoidal rule (modified Euler method) for numerical integration approximates the integral of a function x(t) by summing trapezoid areas as shown in Fig. P2.2-2. Let y(t) be the integral of x(t) .

x(1)4 x(k) x(k+1) KT (k+ 1)T FIGURE P2.2-2 Trapezoidal rule for numerical integration. (a) Write the difference equation relating y[(+1)7]. y(kT), x[(k+1)7], and x(kT) for this rule. (b) Show that the transfer function for this integrator is given by