Ch 11: Integration: Calculus Lesson Plans

About This Chapter

The Integration chapter of this course is designed to help you plan and teach the students in your classroom about integration techniques, anti-derivatives, partial fractions and more. The video lessons, quizzes and transcripts can easily be adapted to provide your lesson plans with engaging and dynamic educational content. Make planning your course easier by using our syllabus as a guide.

Weekly Syllabus

Below is a sample breakdown of the Integration chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.

Day Topics Key Terms and Concepts Covered
Monday Calculating Integrals of Simple Shapes;
Anti-Derivatives: Calculating Indefinite Integrals of Polynomials;
How to Calculate Integrals of Trigonometric Functions
Examples of specific and general trapezoid shapes;
The fundamental theorem of calculus;
An explanation of sine and cosine
Tuesday How to Calculate Integrals of Exponential Functions;
How to Solve Integrals Using Substitution;
Substitution Techniques for Difficult Integrals
A look at how to solve exponential functions;
An outline of the necessary steps;
The process of calculating difficult integrals
Wednesday Using Integration by Parts;
Partial Fractions: How to Factorize Fractions with Quadratic Denominators
Solving examples of integration by parts;
Working with undetermined coefficients
Thursday How to Integrate Functions with Partial Fractions;
Understanding Trigonometric Substitution
The process of using partial fractions;
Examples of trigonometric substitution
Friday How to Use Trigonometric Substitution to Solve Integrals;
How to Solve Improper Integrals
An exploration of techniques for solving integrals;
Identifying and solving improper integrals

12 Lessons in Chapter 11: Integration: Calculus Lesson Plans
Test your knowledge with a 30-question chapter practice test
Calculating Integrals of Simple Shapes

1. Calculating Integrals of Simple Shapes

So you can write something called an integral with a weird squiggly line. Now what? In this lesson, calculate first integrals using your knowledge of nothing but geometry.

Anti-Derivatives: Calculating Indefinite Integrals of Polynomials

2. Anti-Derivatives: Calculating Indefinite Integrals of Polynomials

If you throw a ball in the air, the path that it takes is a polynomial. In this lesson, learn how to integrate these fantastic functions by putting together your knowledge of the fundamental theorem of calculus and your ability to differentiate polynomial functions.

How to Calculate Integrals of Trigonometric Functions

3. How to Calculate Integrals of Trigonometric Functions

Ever feel like you are going around in circles? Like, periodically you have your ups and downs? Well, sines and cosines go up and down regularly too. In this lesson, learn how to integrate these circular functions.

How to Calculate Integrals of Exponential Functions

4. How to Calculate Integrals of Exponential Functions

Exponential functions are so predictable. It doesn't matter how many times you differentiate e^x, it always stays the same. In this lesson, learn what this means for finding the integrals of such boring functions!

How to Solve Integrals Using Substitution

5. How to Solve Integrals Using Substitution

Some integrals are as easy as riding a bike. But more often, integrals can look like deformed bikes from Mars in the year 3000. In this lesson, you will learn how to transform these scary-looking integrals into simpler ones that really are as easy as riding a bike.

Substitution Techniques for Difficult Integrals

6. Substitution Techniques for Difficult Integrals

Up, down. East, West. Opposites are everywhere. In this lesson, learn how you can think of substitution for integration as the opposite of the chain rule of differentiation.

Using Integration By Parts

7. Using Integration By Parts

Your mother may have warned you not to bite off more than you can chew. The same thing is true with integration. In this lesson, learn how integration by parts can help you split a big interval into bite-sized pieces!

Partial Fractions: How to Factorize Fractions with Quadratic Denominators

8. Partial Fractions: How to Factorize Fractions with Quadratic Denominators

Adding fractions with different denominators is something you probably learned how to do in algebra. In this lesson, learn how to do the opposite: take a complicated fraction and turn it into two simpler ones.

How to Integrate Functions With Partial Fractions

9. How to Integrate Functions With Partial Fractions

In this lesson, learn how to integrate complicated fractions by using the partial fractions technique. That is, you will turn a complicated fraction into something a bit easier to integrate by finding partial fractions!

Understanding Trigonometric Substitution

10. Understanding Trigonometric Substitution

Sometimes a simple substitution can make life a lot easier. Imagine how nice it would be if you could replace your federal tax form with a 'Hello, my name is...' name badge! In this lesson, we review how you can use trigonometry to make substitutions to simplify integrals.

How to Use Trigonometric Substitution to Solve Integrals

11. How to Use Trigonometric Substitution to Solve Integrals

In this lesson, we use each of the common integration techniques to solve different integrals. It's not always obvious which technique will be the easiest, so being familiar with an arsenal of methods might save you a lot of work!

How to Solve Improper Integrals

12. How to Solve Improper Integrals

What does it mean when an integral has limits at infinity? These integrals are 'improper!' In this lesson, learn how to treat infinity as we study the so-called improper integrals.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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