The document discusses antiderivatives and some rules for finding them. An antiderivative of a function f(x) is any function F(x) whose derivative is f(x). The power rule can be used to find antiderivatives by adding 1 to the exponent and dividing by the new exponent. Some important rules for finding antiderivatives are the sum and multiple rules, which allow breaking up integrals and pulling constants outside the integral, respectively. Special cases like linear chain rules can also be used when the function would normally require use of the chain rule to differentiate.
An antiderivative of a function is a function whose derivative is the given function. The problem of antidifferentiation is interesting, complicated, and useful, especially when discussing motion.
An antiderivative of a function is a function whose derivative is the given function. The problem of antidifferentiation is interesting, complicated, and useful, especially when discussing motion.
Learn how to learn. Hear are some simple tools and techniques to become an effective learner. Practice the techniques to boost your memory power. Contributed by Moncy Varghese, TOP Academy, Kochi, Kerala, India
International Longitudinal Study of Skills Development in CitiesEduSkills OECD
Social and emotional skills are powerful drivers of well-being and social progress. Children can learn some of these skills which would help them achieve long-term goals, work better with others and manage their emotions. While international research has come up with some measures that can help to improve teaching and parenting practices, they can be better conceptualised and validated.
Knowledge Based Reasoning: Agents, Facets of Knowledge. Logic and Inferences: Formal Logic,
Propositional and First Order Logic, Resolution in Propositional and First Order Logic, Deductive
Retrieval, Backward Chaining, Second order Logic. Knowledge Representation: Conceptual
Dependency, Frames, Semantic nets.
After this presentation students will be able to define
Identify Base, Exponents/Indices, value
Laws of Exponents/Indices
Product law
Quotient law
Power law
Learn how to learn. Hear are some simple tools and techniques to become an effective learner. Practice the techniques to boost your memory power. Contributed by Moncy Varghese, TOP Academy, Kochi, Kerala, India
International Longitudinal Study of Skills Development in CitiesEduSkills OECD
Social and emotional skills are powerful drivers of well-being and social progress. Children can learn some of these skills which would help them achieve long-term goals, work better with others and manage their emotions. While international research has come up with some measures that can help to improve teaching and parenting practices, they can be better conceptualised and validated.
Knowledge Based Reasoning: Agents, Facets of Knowledge. Logic and Inferences: Formal Logic,
Propositional and First Order Logic, Resolution in Propositional and First Order Logic, Deductive
Retrieval, Backward Chaining, Second order Logic. Knowledge Representation: Conceptual
Dependency, Frames, Semantic nets.
After this presentation students will be able to define
Identify Base, Exponents/Indices, value
Laws of Exponents/Indices
Product law
Quotient law
Power law
Iterative constraint solvers work great, but there are cases where we could use better convergence. This presentation explores various Mixed Linear Complementarity Problem (MLCP) solvers and the Featherstone articulated body algorithm and how to mix them.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Thesis Statement for students diagnonsed withADHD.ppt
Section 4.9
1. June 06, 2011
Section 4.9 - Antiderivatives
In other words, F(x) is the antiderivative if the derivative of F(x) = f(x)
Example 1: Find two antiderivatives of f(x) = cos(x)
First solution: F(x) = sin(x) + 5, because F'(x) = cos(x) + 0
Second solution: F(x) = sin(x) - 10, because F'(x) = cos(x) + 0
As you can see, any antiderivative will/can have a constant (+C)
at the end, because when you take a derivative of a constant,
you get 0.
2. June 06, 2011
Taking an antiderivative is like un-doing a derivative.
To take a derivative using the power rule, we multiply by the
exponent then subtract one from the exponent.
So...the "inverse" would be to add one to the exponent, then divide
by the exponent. Theorem 2, states this in mathematical terms.
Let's look at a quick problem. Evaluate
Using the power rule, we will add one to the exponent making it a
4, then we will divide by the exponent. So....
A few rules that help us find antiderivatives
The sum rule just tells us that we can integrate terms separately.
THe multiple rule tells us that if a constant is multiplying out
function, we can bring it outside the integral sign and multiply.
Example 2: Evaluate
First, using the sum rule, we break apart the integral into 3 integrals
Second, we use the multiple rule and bring out any constants
that are multiplying our terms.
Now we can apply the power rule to each term
=
Flip and multiply!
3. June 06, 2011
More flashcards!!! Antiderivatives that
need to be memorized!!!!!
1. 2.
3-8
So far, antiderivates can only be found if we are "un-doing" a
power rule. (If you have a function that requires a power rule to
differentiate, then you can use the power rule for integrals to
find the antiderivative.)
If you are finding an antiderivative of a function that would
require a product/quotient/chain rule to differentiate, then
we do not yet have the tools to find the antiderivative!!!
Special cases: If our function has a "linear" chain rule, we have a
way to find the antiderivative.
Example of the special case (linear chain rule)
(Use the two rules we learned)
k=2 k=3
Both linear chain rules
Notice: THE ANGLES
Answer:
DO NOT CHANGE :)