Construct a C/C++ or Java program for a UNIX environment to use the trapezoidal rule to approximate the integral of f(x) = 1 / (x + 1) for the interval [0 , 2]. This approximation to an integral is called numerical quadrature. Construct your solution so that you compute the areas of n small trapezoids by N individual worker processes. The controller process should spawn N worker processes using the fork and exec UNIX system calls. There should be one pipe with which all N worker processes send results to the controller and N pipes the controller uses to assign a trapezoid to a worker process. Whenever a worker process is ready to compute the area for another trapezoid, it sends the controller a result on the shared "input" pipe. When the controller process receives all the sums from the worker processes, it sums them and prints the answer, along with the amount of time required to obtain the solution, and ignoring the time to set up the processes and the pipes. Experiment with various values of N between 1 and 8 for n = 64 trapezoids. Use a getTime( ) routine to instrument your program so that you can measure the amount of time spent processing your code. Include a suitably large for loop in your procedure to evaluate the area of a trapezoid so that you can measure the time to accomplish the computation. Plot the amount of time versus the value of N used in the approximation.
## Deliverables
1) Complete and fully-functional working program(s) in executable form as well as complete source code of all work done.
2) Deliverables must be in ready-to-run condition, as follows (depending on the nature of the deliverables):
a) For web sites or other server-side deliverables intended to only ever exist in one place in the Buyer's environment--Deliverables must be installed by the Seller in ready-to-run condition in the Buyer's environment.
b) For all others including desktop software or software the buyer intends to distribute: A software installation package that will install the software in ready-to-run condition on the platform(s) specified in this bid request.
3) All deliverables will be considered "work made for hire" under U.S. Copyright law. Buyer will receive exclusive and complete copyrights to all work purchased. (No GPL, GNU, 3rd party components, etc. unless all copyright ramifications are explained AND AGREED TO by the buyer on the site per the coder's Seller Legal Agreement).
## Platform
java or C/C++