# Ch 11: Integration and Integration Techniques: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other calculus work.
- Identify the integration concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our calculus tutoring solution will benefit any student who is trying to learn integration and integration techniques and earn better grades. This resource can help students including those who:

- Struggle with understanding how to calculate integrals of trigonometric and exponential functions, use integration by parts, factorize fractions with quadratic denominators or any other integration and integration techniques topic
- Have limited time for studying
- Want a cost effective way to supplement their math learning
- Prefer learning math visually
- Find themselves failing or close to failing their integration and integration techniques unit
- Cope with ADD or ADHD
- Want to get ahead in calculus
- Don't have access to their math teacher outside of class

## Why it works:

**Engaging Tutors:**We make learning integration and integration techniques simple and fun.**Cost Efficient:**For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.**Consistent High Quality:**Unlike a live calculus tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Learn integration and integration techniques on the go!**Learn at Your Pace:**You can pause and rewatch lessons as often as you'd like, until you master the material.

## Learning Objectives

- Calculate the integrals of simple shapes.
- Calculate the indefinite integrals of polynomials.
- Calculate the definite and indefinite integrals of trigonometric functions.
- Calculate the definite and indefinite integrals of exponentials.
- Use substitution to solve integrals.
- Learn substitution techniques for solving difficult integrals.
- Explain how to use integration by parts.
- Understand how to factorize fractions with quadratic denominators.
- Integrate functions with partial fractions.
- Solve integrals using trigonometric substitution.
- Solve 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

Other chapters within the Calculus: Tutoring Solution course

- Graphing and Functions: Tutoring Solution
- Continuity: Tutoring Solution
- Geometry and Trigonometry in Calculus: Tutoring Solution
- Using Scientific Calculators in Calculus: Tutoring Solution
- Limits: Tutoring Solution
- Rate of Change: Tutoring Solution
- Calculating Derivatives and Derivative Rules: Tutoring Solution
- Graphing Derivatives and L'Hopital's Rule: Tutoring Solution
- Applications of Derivatives: Tutoring Solution
- Area Under the Curve and Integrals: Tutoring Solution
- Integration Applications: Tutoring Solution
- Differential Equations: Tutoring Solution