Calculus 1B: Integration

0 votes
Free Closed [?]
Calculus 1B: Integration

How long should the handle of your spoon be so that your fingers do not burn while mixing chocolate fondue? Can you find a shape that has finite volume, but infinite surface area? How does the weight of the rider change the trajectory of a zip line ride? These and many other questions can be answered by harnessing the power of the integral. 



But what is an integral? You will learn to interpret it geometrically as an area under a graph, and discover its connection to the derivative.  You will encounter functions that you cannot integrate without a computer and develop a big bag of tricks to attack the functions that you can integrate by hand. The integral is vital in engineering design, scientific analysis, probability and statistics. You will use integrals to find centers of mass, the stress on a beam during construction, the power exerted by a motor, and the distance traveled by a rocket.



1. Modeling the Integral




  1. Differentials and Antiderivatives

  2. Differential Equations

  3. Separation of Variables



2. Theory of Integration




  1. Mean Value Theorem

  2. Definition of the Integral and the First Fundamental Theorem

  3. Second Fundamental Theorem



3. Applications




  1. Areas and Volumes

  2. Average Value and Probability

  3. Arc Length and Surface Area



4. Techniques of Integration




  1. Numerical Integration

  2. Trigonometric Powers, Trig Substitutions, Completing the Square

  3. Partial Fractions, Integration by Parts



This course, in combination with Part 1, covers the AP* Calculus AB curriculum.



This course, in combination with Parts 1 and 3, covers the AP* Calculus BC curriculum.



This course was funded in part by the Wertheimer Fund.



Learn more about our High School and AP* Exam Preparation Courses



Calculus 1A: Differentiation



Calculus 1C: Coordinate Systems & Infinite Series



*Advanced Placement and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, these offerings.


Categories:
Starts : 2017-11-01

Comments

Alternatives

-- no alternatives found for the course --
If you know any alternatives, please let us know.

Prerequisites

-- no prerequsites found for the course --
If you can suggest any prerequisite, please let us know.

Paths

No Paths inclusing the course. You can build and share a path with this course included.

Certification Exams

-- there are no exams to get certification after this course --
If your company does certification for those who completed this course then register your company as certification vendor and add your exams to the Exams Directory.

Similar courses

Courses related to the course subject

Teaches, as the antidote to rigor mortis, the art of educated guessing and opportunistic problem solving.

This course covers cutting-edge topics of credit risk management in a rigorous yet inspiring way. The playing field of credit risk…

El Álgebra Lineal es una parte esencial en la formación matemática de todo científico, administrador e ingeniero,…

16 0 0

Algebra+ is a 10-week online course designed for students who have successfully completed high school algebra but who placed into…

Vous voulez apprendre l'algèbre linéaire, un précieux outil complémentaire à vos connaissances acquises dur…

Vous voulez apprendre l'algèbre linéaire, un précieux outil complémentaire à vos connaissances acquises dur…

Vous voulez apprendre l'algèbre linéaire, un précieux outil complémentaire à vos connaissances acquises dur…

Este curso trata la Teoría de Grafos desde el punto de vista de la modelización, lo que nos permitirá con posterior…

From simulating complex phenomenon on supercomputers to storing the coordinates needed in modern 3D printing, data is a huge and g…

Our world is in a data deluge with ever increasing sizes of datasets. Linear algebra is a tool to manage and analyze such data. Th…

Let us know when you did the course Calculus 1B: Integration.

Started on: Completed on:
Your grade (if any):
Comments:

Add the course Calculus 1B: Integration to My Personal Education Path.

Start the course on:
Duration of study:
Notes:

Successfully added to your path.

View your path

Select what exam to connect to the course. The course will be displayed on the exam page in the list of courses supported for certification with the exam.


Notes about how the exam certifies students of the course (optional):