Semester 1 Reflection
A content skill I really enjoyed this year was completing the square to synthesize the integral of a complex, rational function into an arctan. Back in Pre-Calculus, we learned completing the square, but at the time I couldn’t really see the application of this skill, mathematically or in the real world. It was very interesting and surprisingly easy to re-apply this method into a much more complex mathematical skill.
To start this process, we first learned the formula for the antiderivative of an arctan, which is the top line above. Then, after we had done a few straightforward practice problems, we were given the problem below. Then, as you can see, we completed the square in the denominator of the function, which made it possible to apply the arctan formula, which then make it easy to complete the problem.
One of the problem solving skills I need to work on is precision. Particularly with the trigonometric functions, I have problem with making sloppy errors regarding basic things like positives and negatives or accidentally deriving a section of a function instead of integrating. Sometimes, in the rush to finish work in class so I don’t have to take it home, I make mistakes I wouldn’t usually make for the sake of time. To improve upon this, I just need to slow down my work and double check my process to make sure I don’t make small errors. Additionally, reviewing the rules for deriving and integrating trigonometric functions will also help me be more precise in my problem solving.
One of the problem solving skills I need to work on is precision. Particularly with the trigonometric functions, I have problem with making sloppy errors regarding basic things like positives and negatives or accidentally deriving a section of a function instead of integrating. Sometimes, in the rush to finish work in class so I don’t have to take it home, I make mistakes I wouldn’t usually make for the sake of time. To improve upon this, I just need to slow down my work and double check my process to make sure I don’t make small errors. Additionally, reviewing the rules for deriving and integrating trigonometric functions will also help me be more precise in my problem solving.