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Ch 30: PLACE Mathematics: Area Under the Curve & Integrals

About This Chapter

When preparing for the PLACE Mathematics exam, watch the videos in this chapter to refresh your knowledge on definite and indefinite integrals. Also review the average value theorem and the fundamental theorem of calculus to improve your knowledge of the area under the curve and integrals.

PLACE Mathematics: Area Under the Curve & Integrals - Chapter Summary

As part of your preparation for the PLACE Mathematics test, watch these videos on the use of Riemann sums and calculating integrals. In addition to these topics, our instructors also cover:

  • Riemann sums for functions and graphs
  • Limits of Riemann sums
  • Definite integrals, how to calculate them and their linear properties
  • The average value theorem and the fundamental theorem of calculus
  • Indefinite integrals

After each lesson video, complete the corresponding quizzes to fortify your knowledge and discover any areas you don't quite understand. Utilize video tags and lesson transcripts in your review of these areas and ask our instructors any questions you may have to effectively master the material before you take the PLACE Mathematics test.

PLACE Mathematics: Area Under the Curve & Integrals Chapter Objectives

The PLACE Mathematics exam must be completed in four hours and 30 minutes and is a paper-based, multiple-choice test. Of all of the questions on the exam, 19% are part of the calculus and discrete mathematics section. This section is where you could find questions related to the topics in this test. Use these videos and quizzes to prepare for questions on finding the area under a curve and integrals on this test.

8 Lessons in Chapter 30: PLACE Mathematics: Area Under the Curve & Integrals
Test your knowledge with a 30-question chapter practice test
How to Use Riemann Sums for Functions and Graphs

1. How to Use Riemann Sums for Functions and Graphs

A Riemann sum represents an area that is large and complex as the sum of many smaller, simpler areas. Learn how to use Riemann sums for functions and graphs by using the example of determining the size of a piece of land and using multiple areas.

How to Find the Limits of Riemann Sums

2. How to Find the Limits of Riemann Sums

The area, or Riemann sum, is contained by boundaries, known as limits, that can be calculated. Learn about the concept of Riemann sums, where they are used, and how the limits and integrals can be defined mathematically.

Definite Integrals: Definition

3. Definite Integrals: Definition

A definite integral is found as the limit between a line graphed from an equation, and the x-axis, either positive or negative. Learn how this limit is identified in practical examples of definite integrals.

How to Use Riemann Sums to Calculate Integrals

4. How to Use Riemann Sums to Calculate Integrals

Riemann sums use the method of 'slicing' the area of a graph to isolate the equation used to calculate definite integrals. Follow example problems of using Riemann sums to find an area even when divided into different sections.

Linear Properties of Definite Integrals

5. Linear Properties of Definite Integrals

The linear properties of definite integrals allow complex problems to be solved. Learn how to differentiate between and to use the zero integral property, backward property, constant property, additive property, and sums property.

Average Value Theorem

6. Average Value Theorem

The calculation of the average values of equations using integrals can be done using the average value theorem. Learn more about the average value theorem, how to display it on graphs, and how to calculate continuous functions.

The Fundamental Theorem of Calculus

7. The Fundamental Theorem of Calculus

The fundamental theorem of calculus is one of the most important points to understand in mathematics. Learn to define the formula of the fundamental theorem of calculus and explore examples of it put into practice.

Indefinite Integrals as Anti Derivatives

8. Indefinite Integrals as Anti Derivatives

Indefinite integrals, an integral of the integrand which does not have upper or lower limits, can be used to identify individual points at specific times. Learn more about the fundamental theorem, use of antiderivatives, and indefinite integrals through examples in this lesson.

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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