Majority of numerical integration algorithms are written in software and require a long time to initialize and generate results. There is a gradual shift from software-based designs to (Field Programmable Gate Arrays (FPGA)-based designs because they are versatile devices that are increasingly being used as real-time hardware targets in industries. FPGAs are utilized in real-time measurement and control, signal processing, and digital communication, among other applications, because they are inexpensive real-time reconfigurable devices. Because of the high increase in the volume of data used in designs and the large data dependencies in complex computations, researchers are motivated to highlight the need for a shift from the software based implementation of numerical integration to hardware-based FPGAs implementations that are much quicker, more efficient, and more reliable. In this paper, different numerical integration implementations are studied, their strategies discussed, findings assessed and recommendations drawn to enable the suggestion of a better way of improving them. A tabular summary of the review is provided to enhance the understanding of the findings of the review and recommendations for each of the implementations. Based on the review, it can be deduced that FPGAs implementations are faster than software based implementations in C++ and Matlab. It is also evident from the review that architectural designs like pipelining and parallelism when employed on FPGAs greatly improve the throughput of designs and models which significantly reduce data dependencies. It is recommended that FPGA implementation should be employed in the development of numerical integration algorithms due to their low cost, power consumption, small size, and high speed.
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