# Ch 10: Area Under the Curve and Integrals: Homework Help

### About This Chapter

## How it works:

- Identify which concepts are covered on your area under the curve and integrals homework.
- Find videos on those topics within this chapter.
- Watch fun videos, pausing and reviewing as needed.
- Complete sample problems and get instant feedback.
- Finish your area under the curve and integrals homework with ease!

## Topics from your homework you'll be able to complete:

- Using summation notation and mathematical series
- Using Riemann Sums for functions and graphs
- Identifying and drawing left, right and middle Riemann Sums
- Defining the Trapezoid Rule
- Understanding definite integrals
- Understanding linear properties of definite integrals
- Using the Average Value Theorem
- Defining the Fundamental Theorem of Calculus
- Finding the arc length of a function

### 1. Summation Notation and Mathematical Series

The capital Greek letter sigma might be most recognizable as a common symbol in a fraternity or sorority, but it's used for some pretty cool math tricks too. In this lesson, learn how to use sigma for things like determining how many seats are in Michigan Stadium.

### 2. How to Use Riemann Sums for Functions and Graphs

Find out how Riemann sums can be used to calculate multiple areas efficiently. In this lesson, you'll learn how this can come in handy for irregular areas and how you can put it to use.

### 3. How to Identify and Draw Left, Right and Middle Riemann Sums

To overestimate or underestimate? In this lesson, you will draw Riemann rectangles so the right side, left side or middle of the rectangle hits the curve.

### 4. What is the Trapezoid Rule?

In this lesson, you'll move beyond simple rectangles to estimate the area under a curve. Get more sophisticated with your approximations and use trapezoids instead of those pesky rectangles.

### 5. How to Find the Limits of Riemann Sums

What would happen if you could draw an infinite number of infinitesimally thin rectangles? You'd get the exact area under a curve! Define the Holy Grail of calculus, the integral, in this lesson.

### 6. Definite Integrals: Definition

Explore how driving backwards takes you where you've already been as we define definite integrals. This lesson will also teach you the relationship between definite integrals and Riemann sums. Then, discover how an integral changes when it is above and below the x-axis.

### 7. How to Use Riemann Sums to Calculate Integrals

As a new property owner, you might relish mowing your lawn. Up and down your property you mow and measure out small sections to find the area of your property. In this lesson, you will discover what a Riemann sum approach is and how to calculate an estimated area using multiple slices.

### 8. Linear Properties of Definite Integrals

If you're having integration problems, this lesson will relate integrals to everyday driving examples. We'll review a few linear properties of definite integrals while practicing with some problems.

### 9. Average Value Theorem

If you know you've gone 120 miles in 2 hours, you're averaging 60 mph. But what if you know your velocity at every point in time and not how far you've gone? In this lesson, learn how to calculate average values using integrals.

### 10. The Fundamental Theorem of Calculus

The fundamental theorem of calculus is one of the most important equations in math. In this lesson we start to explore what the ubiquitous FTOC means as we careen down the road at 30 mph.

### 11. Indefinite Integrals as Anti Derivatives

What does an anti-derivative have to do with a derivative? Is a definite integral a self-confident version of an indefinite integral? Learn how to define these in this lesson.

### 12. How to Find the Arc Length of a Function

You don't always walk in a straight line. Sometimes, you want to know the distance between two points when the path is curved. In this lesson, you'll learn about finding the length of a curve.

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### Other Chapters

Other chapters within the Calculus: Homework Help Resource course

- Graphing and Functions: Homework Help
- Continuity: Homework Help
- Geometry and Trigonometry in Calculus: Homework Help
- Using Scientific Calculators in Calculus: Homework Help
- Limits: Homework Help
- Rate of Change: Homework Help
- Calculating Derivatives and Derivative Rules: Homework Help
- Graphing Derivatives and L'Hopital's Rule: Homework Help
- Applications of Derivatives: Homework Help
- Integration and Integration Techniques: Homework Help
- Integration Applications: Homework Help
- Differential Equations: Homework Help