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AP Calculus AB: Application and Properties of Definite Integrals

This free online course outlines methods of integration, along with the properties and application of definite integral.

Publisher: ADU
This free online course on Application and Properties of definite integrals describes the mean value theorem and the average value of a function at an interval. The various methods of Integration and the basic rules of Integration. The course also takes you through the basic trigonometric functions. By the end of this course, you will become familiar with the concept of Integration by parts, and a variety of applications of the definite integral.
AP Calculus AB: Application and Properties of Definite Integrals
  • Duration

    3-4 Hours
  • Students

  • Accreditation






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This free online course on Application and Properties of definite integrals introduces you to estimating with the Riemann Sums, Sigma Notation, Properties of a Definite Integral and the Fundamental Theorems of Integral Calculus. In this course, you will learn about the trapezoid approximation methods used in evaluating integrals. Have you ever wondered if there are other aspects of integral calculus? You will learn about the Sigma notation, which is a convenient way to compress writing large sums during Integration. An exciting part of Sigma notation is that they can be used for sums involving subscripts. Another interesting concept will be the three important laws of sigma notation. You will study how to get the exact area under a curve by using an approximation, subintervals and then taking the limit as a function approaches infinity.

The course continues by describing the properties of definite integrals. Do you know that the average set of numbers lies between the smallest and largest number but doesn't have to be a set member? The definite integral enables us to take the average of infinitely many numbers!. The course describes the essence of the Mean Value Theorem for Integrals. You will discuss the relationship between a definite integral and the area under a curve. Have you experienced instances in the application of Integration where the definite integral does not always yield an area under a curve? This is because the basic rules of Anti-differentiation, or Integration. Unfortunately, most expressions occur in a format that doesn't allow for an immediate reversal of the process of differentiation or Integration; therefore, additional methods must be developed. You will be introduced to different methods and techniques used in Integration to solve problems. You will learn how to use a substitution equation for conversions.

Furthermore, knowing how to differentiate the basic trigonometric functions makes the process of finding many integrals involving trigonometric expressions easier. You will learn about the concept of combined sine and cosine functions as well as trigonometric integrals using u-substitutions. You will also be taken through combined tangent and secant functions. Did you know that ​​Trigonometric substitutions can be useful in integrating certain binomials? You will discuss the natural logarithmic functions and Integration by Method of Partial Fractions. In order to use the method of Integration by Partial Fractions, we must first decompose a fractional integrand into the sum of simpler fractions. In conclusion of your study you will be put through a slightly more complicated type of first-order differential equation. If you are a student looking to improve your knowledge of integral calculus and its amazing applications, then register for this course today

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