About This Chapter
How it works:
- Identify which concepts are covered on your area under the curve and integrals in AP calculus 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 Riemann sums for functions and graphs
- Identifying and drawing left, right and middle Riemann sums
- Understanding the Trapezoid Rule
- Finding the limits of Riemann sums
- Using Riemann sums to calculate integrals
- Defining linear properties of definite integrals
- Using Average Value Theorem
- Understanding the relationship between indefinite integrals and derivatives
- Using the fundamental theorem of calculus
- Finding the arc length of a function
1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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 within the AP Calculus AB & BC: Homework Help Resource course
- Functions in AP Calculus: Homework Help Resource
- Graphing and Functions in AP Calculus: Homework Help Resource
- Sequences and Series in AP Calculus: Homework Help Resource
- Limits in AP Calculus: Homework Help Resource
- Continuity in AP Calculus: Homework Help Resource
- Exponentials and Logarithms in AP Calculus: Homework Help Resource
- Exponents and Polynomials in AP Calculus: Homework Help Resource
- Applications of Derivatives in AP Calculus: Homework Help Resource
- Calculating Derivatives and Derivative Rules in AP Calculus: Homework Help Resource
- Differential Equations in AP Calculus: Homework Help Resource
- Graphing Derivatives and L'Hopital's Rule in AP Calculus: Homework Help Resource
- Integration and Integration Techniques in AP Calculus: Homework Help Resource
- Integration Applications in AP Calculus: Homework Help Resource
- Rate of Change in AP Calculus: Homework Help Resource
- Geometry and Trigonometry in AP Calculus: Homework Help Resource
- How to Use Scientific Calculators for AP Calculus: Homework Help Resource