Integrate in a Day

Name: Integrate in a Day
Rating: 4.8 (2 reviews)

A Practical Course in Core Integration Techniques

Created byGary Thomson

Last updated 9/2023

English

What you'll learn

Integration Basics
Integration Techniques
Advanced Integration Techniques
Applications of Integrals

Course content

5 sections • 34 lectures • 6h 13m total length

Antiderivatives7:42
Students will state what the anti-derivative of a function is and will give examples of antiderivatives.
Antiderivatives and Integration10:10
Students will describe the relationship between the antiderivative of a function and an integral.

Notation for Integration12:19
Students will practice the notation used for integration.
The Power Rule14:39
Students will state the power rule for integration and practice using it on relevant functions.
Integratable Form10:40
Students will state forms of functions which are not integratable, will change them to an Integratable form and evaluate the integral.
Integrating the Sine and Cosine Functions8:46
Integration Involving Logarithmic & Exponential Functions11:17
Students evaluate integrals using exponential & logarithmic functions.
Indefinite & Definite Integrals6:46
Students will describe the differences between indefinite and definite integrals.
Evaluating Definite Integrals13:33
Students will state what a definite integral is and will practice evaluating definite integrals.
The Fundamental Theorem of Calculus13:01
Students will state and describe the two versions of The Fundamental Theorem of Calculus.
Test Your Knowledge0:07
Check how much you've learnt about The Power Rule & Other Key Techniques by trying these practice questions. Remember to check your work against the step by step solutions provided.

Integration by U-Substitution18:09
Students will describe functions which can be integrated using a substitution method and will practice the technique.
The Chain Rule11:06
Students will confidently use the reverse chain rule to integrate composite functions.
Integration by Parts17:59
Students will state when integration by parts should be used and will practice the technique.
Integration by Parts for Definite Integrals14:49
Students will use the integration by parts technique to evaluate relevant definite integrals.
Partial Fractions16:17
Students will learn techniques for working with partial fractions in preparation for integration using partial fractions.
Integration using Partial Fractions19:03
Students will use partial fractions to change a function to an integratable form and then evaluate the integral.
Improper Integrals4:56
Students will state what an improper integral is and give examples of improper integrals.
Evaluating Improper Integrals 111:33
Students will evaluate one form of improper integral using a limit technique.
Evaluating Improper Integrals 210:47
Students will evaluate one form of improper integral using a limit technique.
Evaluating Improper Integrals 314:50
Students will evaluate one form of improper integral using a limit technique.
Evaluating Improper Integrals 413:46
Students will evaluate one form of improper integral using a limit technique.
Test Your Knowledge0:07
Check how much you've learnt about The Chain Rule & Advanced Techniques by trying these practice questions. Remember to check your work against the step by step solutions provided.

Riemann Sums9:52
Students will describe what a Riemann sum is and how they can be used to approximate the area under a curve.
Riemann Sums and Integrals7:42
Students will describe how a Riemann sum can be used to exactly represent the area under a curve using a limit.
Finding the Area Under a Curve16:51
Students will use definite integrals to find the area between a curve and the co-ordinate axes.
Finding the Area Between Two Curves18:59
Students will form and evaluate definite integrals to find the area between two curves.
Volumes of Revolution Around the X-Axis11:57
Students will practice finding volumes of revolution around the X-Axis by setting up and evaluating the relevant definite integral.
Volumes of Revolution Around the Y-Axis16:44
Students will practice finding volumes of revolution around the Y-Axis by setting up and evaluating the relevant definite integral.
Arc Length Using Integration9:09
Students will describe how integration can be used to find the length of an arc in preparation for evaluating arc length.
Evaluating Arc Length Using Integration19:56
Students will use integration to find the length of an arc generated by a smooth curve.
Test Your Knowledge0:06
Check how much you've learnt about Applications of Integrals by trying these practice questions. Remember to check your work against the step by step solutions provided.

Requirements

Differential Calculus
Experience with Trigonometry would be an advantage

Description

This Course is For You

I created this course for you because I know it's difficult to be on top of your studies all of the time. There are so many reasons why you might need to catch up:

· You missed an important class (or don't attend a class!)

· You didn't understand something in class

· You found a topic particularly challenging

· You need to review for a test

· You need to access relevant practice questions

Whatever your reason this course will quickly transform your integration skills and get you ready to ace your next assignment!

What You'll Take Away From This Course

Integration is a huge topic with many applications but it can be broken down in a small number of core techniques which, once mastered, can be applied to answer many question types. Each instructional video teaches one core technique and focuses on example questions more than theory. You will then practice what you've learnt in the extensive end of section review exercise. We've also included step-by-step solutions so you can check your work as you go. Take this course and you will learn:

· Key integration techniques such as the power rule and integration by parts

· The reverse chain rule and advanced techniques such as improper integrals

· Indefinite and definite integrals

· Applications of integrals such as areas under curves and volumes of revolution

Take this course and you will be able to integrate in a day!

Who this course is for:

Students who need to learn to integrate quickly
Students reviewing key integration techniques for a test or assignment
Students looking for relevant practice questions with full step-by-step solutions

Integrate in a Day

What you'll learn

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Course content

Defining the Integral (Optional)2 lectures • 18min

The Power Rule & Other Key Techniques9 lectures • 1hr 31min

The Reverse Chain Rule & Advanced Techniques12 lectures • 2hr 33min

Application of Integrals9 lectures • 1hr 51min

Additional Resources2 lectures • 1min

Requirements

Description

Who this course is for: