Design and implement a class Sample that models a sample as explained above. The function to be sampled is given as y = 2 · x + 3, whereas the initial sample point, the interval and the number of samples are variables with different values for each instance of class Sample.

Fit the class with the following public methods:

• a suitable constructor;
• "getter methods" that return the initial sample point, the interval and the nummber of samples;
• a method samplePoint: given an integer i it should return the i-th sample point;
• a method sampleValue: given an integer i it should return the i-th sample value;
• a method toString: it should return a string of n lines separated by the new line character \n; the i-th line should hold the i-th pair of sample point and sample value, seperated by a space.

Solution: Sample.java

Part 2

Implement a class SampleTools. It should include a public, static method integrate, that accepts a Sample object as parameter and computes an approximation of the integral of the sampled function in the interval [x₀, x_n-1] by adding all sample values for i = 0, ..., n-1 multiplied by the sample interval d_x according to the summation formula:

This method just computes the rectangle's area as shown in the figure, which is an approximation to the integral:

Solution: SampleTools.java

Part 3

Implement a client class Client with a main method that asks the user to enter the initial sample point, the sample interval and the number of samples. The programm should create a instance of Sample. It should then call toString on the instance to print the samples.
Finally, it should compute and print the integral approximation of the sampled function.

Solution: Client.java

Part 4 (Note: the solution of this part requires the use of inheritance

Implement two classes SquareRootSample and SineSample, each derived from class Sample. The new classes should redefine the method sampleValue in order to return the values of y = sqrt(x) and y = sin(x) respectively.

Implement a client class Client2 with a main method that asks the user to enter the initial sample point, the sample interval and the number of samples. The programm should create an instance of SquareRootSample and one of SineSample. It should then call toString on each instance to print the samples.
Finally, it should compute and print the integral approximation for each of the two sampled functions.

Solutions: SquareRootSample.java, SineSample.java, Client2.java