Name: Integration Basics - The Meaning of the Integral
Uploaded: 2022-10-05T03:14:47.000Z
Duration: 19 min
Description: This video explains what an integral means and where the notation comes from. Several example problems highlight how to apply and use the meaning of the integral.

This video explains what an integral means and where the notation comes from. Several example problems highlight how to apply and use the meaning of the integral.

Math

While teaching high school calculus for 15+ years, I used to joke that I was a “teacher by day and juggler by night.” I’ve spent a lot of time performing as a juggler and have always said that street performing was the best professional development I’ve ever had since students are basically hecklers. Now, I’m a “father by day, and teacher by night.” I’m here to help those struggling “students by night”. I’ve had a lot of success guiding and preparing high school math students and I want to continue to serving them as they navigate the problem solving process. I believe every student can be successful when they have the right guide. 

Integration Basics - The Meaning of the Integral

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Calculus & math doesn't need to be difficult - you just need the right guide. I've helped students succeed on the AP BC Calculus Exam for 15+ years and most of my students score a 4 or 5. I'll explain things in simple ways and provide strategies that will help you successful. I use research-based learning science and experience as a semi-professional juggler performer that will help you learn and cultivate your motivation.

Mr. Owsley is one of the best math teacher I have met in my life time. I have taken his Calculus BC class when I was a high school student. His class was interactive, inspiring and creative. He impacted me not only mathematically, but also as a human being in shape and form. I am currently a PhD student in math, and I am much in debt in the math education I received from Mr. Owsley. Despite of the fact that I have had a lot of math teachers on my way of doing mathematics, he remains one of my favorite, most inspiring, and motivating teacher. He explains problems with such a passion and clarity that I think his classes are very helpful to students working on the topic of calculus. I will very much recommend working with him through the way of calculus and other mathematical topics.

This is a video explanation of the 2023 BC Calculus FRQ #6. This problem covers topics of series including Taylor polynomials & the Lagrange Error Bound.

2023 BC Calculus Free Response Question #6 (Series)

This is a video explanation of the 2023 BC Calculus FRQ #5. This problems covers various aspects of the application of the integral.  Topics that are discussed include area between curves, improper integrals and integration by parts. The video does not cover volumes of revolution.

2023 BC Calculus Free Response Question #5 (Applications of the Integral)

This is a video explanation of the 2023 BC Calculus FRQ #4. The video covers the topic of interpreting the graph of a derivative. It also includes L'Hospital's rule and finding absolute minimum values.

2023 BC Calculus Free Response Question #4

This is a video explanation of the 2023 BC Calculus FRQ #3. This video covers the topic of Differential Equations including slope fields, linear approximation and separating variables.

2023 BC Calculus Free Response Question #3 (Differential Equations)

This is the video solution to the 2023 BC Calculus FRQ#2. The question covers the topic of Vectors.

2023 BC Calculus Free Response Question #2

This is a video explanation of the 2023 BC Calculus FRQ #1.  This question covers topics of applying calculus to tables, Riemann sums, and average value.

2023 BC Calculus Free Response Question #1 (Table Problem)

A useful integration technique leverages the trigonometric reduction formulas. Watch this short video for some examples of how to use the half-angle formulas and other trigonometric formulas to solve specific types of integrals. 

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BC Calculus Free Response Question Taylor Series (2021)

Using a table of values to solve BC Calculus questions is a frequent question type on the BC Calculus Exam. This is a video explanation of the 2021 BC Calc Table Problem.

BC Calculus Free Response Question Table Problem (2021)

Problems involving volumes of revolution often occur on the BC Calculus Exam (although not as frequently now as they did 10 years ago). This is a video explanation of the 2021 problem.

BC Calculus Free Response Question Volumes of Revolution (2021)

The BC Calculus Exam often includes problems based off of a given rate function. This is a video explanation of the 2022 Rate Function problem.

Greg O.

Integration Basics - The Meaning of the Integral

Greg's Math videos

2023 BC Calculus Free Response Question #6 (Series)

2023 BC Calculus Free Response Question #5 (Applications of the Integral)

2023 BC Calculus Free Response Question #4

2023 BC Calculus Free Response Question #3 (Differential Equations)

2023 BC Calculus Free Response Question #2

2023 BC Calculus Free Response Question #1 (Table Problem)

Trig Reduction Formulas with Integrals

BC Calculus FRQ Differential Equation Problem (2021)

BC Calculus Free Response Question Taylor Series (2021)

BC Calculus Free Response Question Table Problem (2021)

BC Calculus Free Response Question Volumes of Revolution (2021)

BC Calculus FRQ Rate Function (2022)

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2023 BC Calculus Free Response Question #4

2023 BC Calculus Free Response Question #3 (Differential Equations)

2023 BC Calculus Free Response Question #2

2023 BC Calculus Free Response Question #1 (Table Problem)

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