For this problem, I had to recognize that the derivative of sinx was cosx. This allowed me to substitute out the sinx and integrate it into one of the inverse trig functions. I realized that I could replace sinx with x and it would match the formula for the derivative of arctanx. Therefore, I was able to plug in the sinx into the arctan equation and successfully integrate the problem. My growth this these types of integrals was realized when I was given a test on this subject, and I was able to successfully solve the problems and achieve an A.

During this semester of Calculus II, I have refined my ability to tackle real-life problems and utilize the mathematical skills I have acquired to solve these problems. As part of the Calculus II curriculum, we are assigned problems of the week, which are reality based, logic puzzles designed to test our ability to analyze real-life problems and devise an effective solution.

One POW assigned involved eight people arranged in a circle who each flipped a single coin. I was tasked with finding the probability that no two next to each other flipped heads. Once I read the problem, I instantly drew a diagram for the problem and formulated a strategy for solving the POW. Eventually, I came with the solution of calculating the number of combinations which had no adjacent people standing up and was able to convert that into a percentage chance of that situation occurring. POWs and other mathematical problems applicable to the real world further improve my ability to apply my knowledge to real world situations and generate solutions to complex problems. In order to expand upon this ability, I will analyze almost every mathematical skill I learn and attempt to understand its real world applicability and how it will aid me in my life. The ability to not only retain the mathematical knowledge I learn in Calculus II but also to apply it to the real world is an invaluable skill I have acquired. The most valuable asset I have gained from this class is to not be a mathematical thinker, but a mathematical doer.

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