Ch 46: MTTC Math (Secondary): Integration & Integration Techniques

About This Chapter

The video lessons in this chapter cover integration and integration techniques. Use the videos to gather more knowledge and to prepare to answer pertinent questions when you sit for the MTTC Math (Secondary) examination.

MTTC Math (Secondary) Integration and Integration Techniques - Chapter Summary

The engaging video lessons in this chapter will remind you of how to check integration by substitution and solve complicated fractions. The video topics include definite integrals, composite functions, the fundamental theorem of calculus and Riemann sums. Watch the parts of the lessons that you need to review as you get ready to take the MTTC Math (Secondary) examination. This chapter could assist you with:

  • Writing integrals of simple and complex shapes
  • Working with indefinite integrals of polynomials
  • Calculating integrals of exponential and trigonometric functions
  • Integrating sine and cosine
  • Using substitution to solve integrals
  • Identifying substitution tips to use with difficult integrals
  • Utilizing the product rule and integration by parts
  • Dividing complicated fractions into partial fractions
  • Using 'u' substitution and trigonometric substitution
  • Solving improper integrals

Review integration and integration techniques with the assistance of educated mathematics instructors whose direct approach make the concepts easier to absorb. The chapter's self-paced online videos include clickable links for further exploration of key terminology. Refer to the written transcripts or use the video tags to find information in the lessons. Self-assessment quizzes and a multiple-choice chapter examination are included.

MTTC Math (Secondary) Integration and Integration Techniques Objectives

Accounting for 28% of the questions, the 'Patterns, Algebraic Relationships and Functions' section of the four-part MTTC Math (Secondary) examination will assess your capacity to understand and apply integration techniques. Recall your review of this chapter and your answers to quiz questions as you demonstrate your proficiency and qualifications to teach these and other mathematics topics in Michigan schools.

As a candidate for a teaching endorsement, you'll have the opportunity to test by computer or on paper. You must answer all questions within two hours and 30 minutes if you take the computer-based examination. A time limit of four hours and 30 minutes applies if you take the paper-based version of the test. Regardless of the version you choose, you'll find 80 multiple-choice questions on the examination.

12 Lessons in Chapter 46: MTTC Math (Secondary): Integration & Integration Techniques
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.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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