Calculus 1B: Integration

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edX online courses
Harvard University, the Massachusetts Institute of Technology, and the University of California, Berkeley, are just some of the schools that you have at your fingertips with edX. Through massive open online courses (MOOCs) from the world's best universities, you can develop your knowledge in literature, math, history, food and nutrition, and more. These online classes are taught by highly-regarded experts in the field. If you take a class on computer science through Harvard, you may be tau...
Harvard University, the Massachusetts Institute of Technology, and the University of California, Berkeley, are just some of the schools that you have at your fingertips with edX. Through massive open online courses (MOOCs) from the world's best universities, you can develop your knowledge in literature, math, history, food and nutrition, and more. These online classes are taught by highly-regarded experts in the field. If you take a class on computer science through Harvard, you may be taught by David J. Malan, a senior lecturer on computer science at Harvard University for the School of Engineering and Applied Sciences. But there's not just one professor - you have access to the entire teaching staff, allowing you to receive feedback on assignments straight from the experts. Pursue a Verified Certificate to document your achievements and use your coursework for job and school applications, promotions, and more. EdX also works with top universities to conduct research, allowing them to learn more about learning. Using their findings, edX is able to provide students with the best and most effective courses, constantly enhancing the student experience.

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22043 reviews

Course Description

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

...

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.

Reviews 9/10 stars
11 Reviews for Calculus 1B: Integration

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Cameron Brenke profile image
Cameron Brenke profile image

Cameron Brenke

10/10 starsCompleted
2 years, 5 months ago
An absolutely excellent course. Between the available Calculus courses on Coursera and Edx, this is by far the best. The questions are challenging on a level far beyond any other. When you are done with this course there won't be any problem you won't be able to answer.
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V R profile image
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V R

10/10 starsCompleted
3 years, 1 month ago
One of the best online courses on this subject. The best part of this course are the problems which attempt to build intuition in steps. Don't miss these even if you are only auditing this course. Looking forward to 1C
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Phi Luu profile image
Phi Luu profile image

Phi Luu

10/10 starsCompleted
3 years, 1 month ago
Extremely good course! This course taught me a lot of thing about integration. It made "Integral" closer to me, not so far like I learned in my old country. In fact, I didn't know why we learn Calculus then. It wasn't until I took this series courseware of MIT. The course has a perfect flow of lessons and interesting problem set, which helps students interface Integral slowly and carefully, step-by-step. It actually blew my mind, and I learn many things from this course. I sincerely thank Prof. Jerison, Prof. Staffilani, Dr. French, and Dr. Chu for making this real! FIVE STARS FOR THE COURSE!
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Yanto Jakop profile image
Yanto Jakop profile image

Yanto Jakop

10/10 starsTaking Now
3 years, 1 month ago
I have taken about 10 MOOCs in Coursera and edX so far, and I have to say this is the best course that I have seen! The content is in-depth, well-structured. The instructors are clear at giving step-by-step explanations to not-so-easy-to-understand concepts. Especially loves the quizzes that allows us to key in any expressions and even sketch graphs, and the grading can be done automatically! (I guess should have some AI involved). The content and quiz questions were very challenging. As an instructor of this topic at my institution, I still need to spend 4-6 hours per week going through the materials. Overall, an excellent course. I wish I could gain the experience of going through this MOOC to teach this topic. Thanks MIT!
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Phi Luu profile image
Phi Luu profile image

Phi Luu

10/10 starsCompleted
3 years, 1 month ago
This course is excellent! It's much much better than the previous course (Calculus 1A: Differentiation). Contents, Instructors, and Providers are outstanding! This course helps me understanding deeply into integration (deep enough). I learned from this course not only the techniques of integration but also how to apply Calculus to the real world.
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Student

10/10 starsCompleted
3 years, 1 month ago
This is a damn hard course that you're going to have to put a lot of time into if you want to do well. The edX forums are not perfect, but the staff and other students are very helpful and everyone takes time to help each other out. You'll do fine If you don't get too hung up on not being able to solve some problems — even students at MIT don't ace this course.
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Anonymurs Liu profile image
Anonymurs Liu profile image

Anonymurs Liu

10/10 starsTaking Now
3 years, 2 months ago
Incredible course. For some special reason, our university did not offer calculus when I was doing the bachelor, and I was stupid then that I did not get myself involved in calculus. And this course is really awesome. with 10~20 hours spent in it every week, it greatly increased my understanding of math or even other aspects of life. By the way, Calculus II seem to be more challenging than calculus I
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Ravi Pendurthi profile image
Ravi Pendurthi profile image

Ravi Pendurthi

10/10 starsTaking Now
3 years, 5 months ago
May be i can understand better about science by this. Helps to solve so many since problems like quantum mechanics. Expressing our ideas in better mathematical way.
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Carlos Morales profile image
Carlos Morales profile image

Carlos Morales

10/10 starsTaking Now
3 years, 5 months ago
MIT EDX Differential Calculus was the better math course I have ever taken, I took Calculus I in Coursera but it was too basic, too far of the level MIT Calculus. I hope this new MIT Integral Calculus course will be so good as MIT Differential Calculus course.
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Oleksii Sirotkin profile image
Oleksii Sirotkin profile image

Oleksii Sirotkin

10/10 starsCompleted
3 years, 7 months ago
I am completed the Calculus 1A: Differentiation and it has a best workflow and formalization I ever seen (the best of about 20 courses I take before). Hope Calculus 1B: Integration be on the same level or a better.
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Zaz Brown profile image
Zaz Brown profile image

Zaz Brown

1/10 starsTaking Now
3 years, 7 months ago
If it's anything like 18.01.1x, this is terrible. Material is confusing and has many mistakes, instructors are humorless and impatient, and edX has many bugs. Would strongly recommend taking Ohio State's ‘Calculus 1’ on Coursera instead. 18.01x is the worst online course I've taken so far.
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