Integral

Integrals have been around for hundreds of years and have been used in several ways to solve complicated math problems. An integral is a function that expresses the area under the curve of a graph of a function. The first time the technique was brought forward was by a greek astronomer Eudoxus in the 370 BC. He used the technique called as the method of exhaustion which helped him find area or volume. The way he achieved this was using infinite numbers of division. Later Archimedes came along in the 3rd century BC and used the method of exhaustion to find the area of parabolas and even the area of a circle. Cavalier came later on and found the Cavalier quadrature formula but by the most recent evolution of integrals because the fundamental…

integrable functions was always valid and therefore, gave validation to Fourier’s proof of his series. What is now considered to be one of Lebesgue’s greatest contribution was his work with the Riemann integral. Before his work, the Riemann method was only applicable to continuous functions with a few exceptions. Lebesgue’s work is considered of great importance because it led to the generalization of this integral. In other words, he was able to formulate a new method of measure and gave a new…

they become “stuck in the past,” frozen in time, and unable to move forward. Becoming “frozen in the past” is something that occurs on a biological level, as well as on a psychological one. Despite living in “the after,” the body of a trauma survivor may continue to pump out stress hormones, as if the event were still taking place. This in and of itself, outlines the paradox of trauma, and the area where most healing needs to take place. Moving on involves recognizing what has happened, grieving…

Fundamental Theorem of Calculus The Fundamental Theorem of Calculus evaluate an antiderivative at the upper and lower limits of integration and take the difference. This theorem is separated into two parts. The first part is called the first fundamental theorem of calculus and states that one of the antiderivatives of some function may be obtained as the integral of the function with a variable bound of integration. The second part of the theorem, called the second fundamental theorem of…

I have a memory of sitting in my elementary classroom doodling on a page on my desk and uninterested in what the teacher was teaching. Suddenly I look up from my doodles and realize that the teacher has moved on to a new subject and I have no clue what is happening. Some elementary school teachers move from subject to subject throughout the day and hope that the students are able to jump from subject to subject with the teacher. There is now an instructional method that allows the teacher to…

Khloe Kardashian is showing her true feelings for Lamar Odom ever since he fell unconscious at a Las Vegas brothel. Hollywood Life shared that Khloe has actually been showing a lot of compassion for Lamar during this time. She has been by his bed and sources say that Khloe Kardashian has even been holding Lamar’s hand and kissing him on the cheek during this hard time. Khloe is showing how she feels about Lamar and it has everyone wondering if these two could be on the verge of reuniting. This…

An internal code of conduct creates an objective standard that can be followed by those within social media. Specifically it seems that these internal processes clearly illuminate the need in which to take out any subjective action, as this can affect the brand of the company. It is important to ensure that this level of effectiveness is applied to prevent any negative action from occurring. The code of conduct plays an integral role in terms of identifying a standard that can be used to promote…

In the book The Integration of Psychology and Theology, Carter and Narramore present several aspects and issues regarding the integration of Psychology and Theology. The main focus of the book revolves around four different models of integration. The four models are; the against model, the of model, the parallels model, and the integrates model. The first chapter of the book focuses on people’s thoughts and perceptions on the idea of integrating psychology and theology. One of the main…

INTEGRATED CURRICULUM APPLICATION LESSON REFLECTION 1. What were your concerns prior to teaching your Integrated Lesson? I had many worries that came with this integrated lesson, but I would have to say my biggest concern was that I was going to have a hard time controlling the volume during this activity. The activity was very interactive and involved a price for the winning team. I thought this might cause some tension and craziness but it ended up going just fine and the children were very…

constant on I. This is the converse of the property of the derivative of a constant. The derivative of a constant function is zero. Therefore, if we have the derivative of any function being zero it is well understood that it is a constant function. Second theorem: Assume f is continuous on an open interval I, and let P be an anti-derivative on I. Then, for each c and each x in I, we have P(x)=P(c)+∫_c^x▒f(t)dt If P is an anti-derivative of f , then the term ∫_c^x▒f(t)dt , will yield P(x)-P(c).…