Problem 1. Integration
Create a program to integrate an arbitrary time-domain signal, with variable limits of integration and variable sample interval . Test your program on a simulated time-domain signal.
Problem 2. Differentiation.
Create a program to compute the derivative of an arbitrary input function, with arbitrary duration and arbitrary limits. Remember to check that you start computing at least at the second data point. Test your program on a simulated time-domain signal.
Problem 3. Create a program that prepares an arbitrary sinusoidal waveform with parameters input from the user (via file or keystroke), passes the signal to a function that performs integration and differentiation and receives the result and writes it to a file.
Problem 4. Create a program to perform an automated search of an input file and output the number of prime numbers contained in that file.