The trapezoidal rule for numerical integration is defined in Figure. The value of the inte...

The trapezoidal rule for numerical integration is defined in Figure. The value of the integral at t = kT is equal to its value at t = (k – 1) T plus the trapezoidal area shown.

(a) Write a difference equation relating y[k], the numerical integral of x(t), to x[k] for this integrator.

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(b) Write a MATLAB program that integrates  with T = 0.1 s, using trapezoidal integration.

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(c) Run the program in Part (b), and verify the result.