CLEP Calculus: Integral Calculus and Applications

This material has been specifically designed to teach you about the various methods and applications of integration. Are you aware that there are two types of integrals? You will be introduced to their properties, differences and applications. You will learn about the concepts of integration and the constant of integration. The relationship between Riemann sums and calculating the area under a curve is highlighted. You will also be introduced to the functions of Sigma notation along with its various formulas. When working with a variable number in calculus, it is important to understand the dummy variable and stopping point. The multiple formulas for sums of sequences are explained. Did you know that there are three sigma laws to simplify calculations?

Two important concepts to understand are the average value of a function on an interval and mean value theorem for integrals. The power rule and basic rules of integration will be covered extensively. U-substitution allows for an immediate reversal of the process of differentiation; learn how to find integrals using the u-substitution method. This course teaches you how to integrate the six trigonometric functions. When integrating certain binomials, trigonometric substitutions can be useful. You will also be able to discuss integration using lnx if you are working with natural logarithmic functions. Knowing how to decompose a fraction into simpler functions is also imperative in calculus. Examine how to integrate partial functions. There is also a slightly more complicated type of first order differential equation. This course teaches you about separable differential equations. You will also be able to explain the technique of integration by parts.

Furthermore, you will see how to integrate inverse trigonometric and natural exponential functions. Examine how to find the area above and below the x-axis. The volume of a solid of revolution, as well as with a known cross section, will also be covered. The formula for the area of a region in a plane will also be explained. You will understand the surface of revolution and how to find the arc length. Exponential growth and decay are key concepts in calculus and you will become familiar with their various applications.