CLO2. Use integration techniques on single and multi-variable functions
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Module 1: Basic Integration Formulas
This module will familiarize you in the application of integration formulas for single and multi-variable functions such as involving algebraic, trigonometric, logarithmic, exponential, and inverse trigonometric functions.
In this module, I realize the true meaning of anti-differentiation which is the reverse process to differentiation. It is a process of solving antiderivatives that are the opposite of derivatives. This antiderivative is a function that reverses what the derivative does. One function has many antiderivatives, but they all take the form of a function plus an arbitrary constant.
Antiderivatives are a key part of indefinite integrals. An indefinite integral pertains to a function that takes the antiderivative of another function. It is visually represented as an integral symbol, a function, and then a dx at the end. The integrals are generally classified into two types which are the definite integral and this indefinite integral. However, the thing that makes indefinite integral different from definite integral is the fact that this integral does not have any upper and lower limit compared to the definite integral that has it. Also, the process of finding indefinite integral is called integration.
One problem that was stuck in my mind in this classwork assignment would be item #8 in classwork assignment 3 which is regarding trigonometric functions. I find it hard to answer because there is the presence of fraction sign as well as combination of different trigonometric wordings such as sine and cosines. However, because of the guided formulas, I was able to arrive to the final answer with a sufficient knowledge to make sure that my answers are correct.
It is evident in this topic that I use integration techniques on single and multi-variable functions. As it is one of the early topics, I find myself engaged based on the reflective learnings that I had in this topic.
Aside from that, it is now reflected in my mind that there are different formulas that are needed to solve for the antiderivatives such as power formula, trigonometric function formulas, logarithmic function formulas, exponential function formulas, inverse trigonometric function formulas, as well as hyperbolic function formulas.
Aside from indefinite integrals, I also learned the idea regarding definite integrals. To explain, the definite integral can be solved by evaluating the difference between the values of the integral of a given function for an upper value and a lower value of the independent variable. In this type of integral, we do not need to add arbitrary constant as indefinite integral does.
Overall, in this module, I learned the basics regarding the integration formulas that I can use in future topics.
One problem that was stuck in my mind in this classwork assignment would be item #10 in classwork assignment 7 which is regarding hyperbolic functions. I find it a little bit hard to answer despite the fact the it is just with the concept in trigonometric functions, the presence of h makes it quite complicated and because there is the presence of fraction sign as well as combination of different trigonometric wording such as sine h. At first glance you will find the equation simple but to answer it, you will encounter a lot of loopholes which needs to be filled. However, because of the guided formulas, I was able to arrive to the final answer with a sufficient knowledge to make sure that my answers are correct.
It is evident in this topic that I use integration techniques on single and multi-variable functions. As it is one of the early topics, I find myself engaged based on the reflective learnings that I had in this topic.
Module 2: Other Integration Formulas
This module deals with the integration of hyperbolic functions, application of general power formula and definite integrals.
In this module, I realize that integration can be done in different aspects, and with the incorporation of the basics, we can easily adhere to this kind of topic because of that idea. As for my learnings, it is reflected in mine that there are other integration formulas that are needed such as integration by parts, trigonometric integrals, trigonometric substitution, as well as rationalizing substitution.
We also have improper integrals, I also learned the idea regarding improper integrals. To explain, an improper integral is a definite integral in which one or both limits are infinite or an integrand that approaches infinity at one or more points in the integration range. In addition, improper integrals cannot be calculated with normal Riemann integrals.
Overall, in this module, I learned that the idea regarding integration is not that simple as it needs more analysis from one point in order to arrive to another point, and that is what I did in here, getting prior knowledge about the first major topic, to easily went through this next major topic.
One problem that was stuck in my mind in this classwork assignment would be item #10 in classwork assignment 3 which is regarding trigonometric substitution. I find it a hard to answer despite the fact the it is just with the concept in trigonometric functions, the presence of formulas makes it quite complicated and because there is the presence of rational fraction sign as well as combination of different trigonometric wording such as secant and tangent. At first glance you will find the equation simple but to answer it, you will encounter a lot of loopholes which needs to be filled. However, because of the guided formulas, I was able to arrive to the final answer with a sufficient knowledge to make sure that my answers are correct.
It is evident in this topic that I use integration techniques on single and multi-variable functions. As it is one of the early topics, I find myself engaged based on the reflective learnings that I had in this topic.
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