1. Given that calculators or websites like Wolfram Alpha can compute an integral for you, what benefits are there toknowing the techniques of integration presented in the chapter?

Here is the initial problem with calculators or websites like Wolfram Alpha, etc. Although yes, the calculator is able to compute and integral, however, understanding its actual applied instance and taking the environment into consideration is not something that is so easy. These are tools that are made to help aid mathematicians, and others that would be interested in utilizing these types of mathematical tools, or simulating the mathematical existence of the actual variables within the environment. The benefits there are to actually knowing the techniques of integration are understanding the outside systems that are involved as well as understanding how the actual components of the equation to the different rules that we are given to use within the spectrum of the given problem, such as a word problem. Another problem that I have found that I usually end up having is that a lot of the calculators are difficult to put the correct paramaters into, so even though I can use the calculators to efficiently help myself learn and do work, it is often increasingly hard to find the correct way to actually interate the kind of problem I am trying to solve, especially the more complex the equations get.

2.Give at least oneexampleof a use for integration in your major/concentration/degree program,or for your job.

One massive example of a use for integration in my MsC. in Computer Science is for signal processing. Integrals can be used to compute the area under a signal which is useful for audio and speech recognition, as well as image processing, video processing, and data compression. A more in depth understanding an application of these mathematical parameters can help us wholey optimize the field as well as apply different types of optimization algorithms and machine learning algorithms to this field to help the exponential growth of our applications.

reply to the above