About This Chapter
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
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.
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.
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.
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!
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.
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.
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!
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.
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!
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.
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!
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.
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Other chapters within the Calculus Syllabus Resource & Lesson Plans course
- Graphing & Functions: Calculus Lesson Plans
- Continuity: Calculus Lesson Plans
- Geometry & Trigonometry: Calculus Lesson Plans
- Using Scientific Calculators: Calculus Lesson Plans
- Limits: Calculus Lesson Plans
- Rate of Change: Calculus Lesson Plans
- Calculating Derivatives: Calculus Lesson Plans
- Derivative Graphs & L'Hopital's Rule: Calculus Lesson Plans
- Applications of Derivatives: Calculus Lesson Plans
- Area Under the Curve & Integrals: Calculus Lesson Plans
- Integration Applications: Calculus Lesson Plans
- Differential Equations: Calculus Lesson Plans