AP Calculus BC: Integration
This free online course describes the methods of integration and the applications of definite integral in calculus.Publisher: ADU
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AP Calculus BC: Integration is a free online course that will take you through the concept of integration and various methods of integration. Integration can be used to find areas, volumes and other useful things. It is the way of adding parts to find the whole. Integration can be used to solve two essentially different types of problems. The first type are problems where the derivative of a function, its rate of change or the slope of its graph, is known. In finding such problems, it is required that the process of differentiation is reversed. This reverse process is known as antidifferentiation (Integration) or finding an indefinite integral. The second type are problem involves adding up a very large number of very small quantities. This process leads to the definition of the definite integral and its properties. This course illustrates how to solve for the average value of a function on an interval as well as the mean value theorem for integrals.
If you want to learn about the first and second fundamental theorem of integral calculus, this course comes highly recommended. It covers in detail power rules and basic rules to assist in integration. Unfortunately, most expressions in calculus are given in a format that doesn't allow an immediate reversal for the process of differentiation. Therefore, additional methods must be developed. One such powerful method is the world-famous method known as u-substitution. Let’s assume you are asked to break a broomstick and a bunch of broomsticks respectively. Which will be easier to complete? Of course, the broom stick! The process of integration goes from the easier aspect to the more difficult aspect. However, the content of this course will make your learning process easy, detailed and interesting. Knowing how to differentiate the six basic trigonometric functions streamlines the process of finding many integrals involving trigonometric expressions. Since finding the integral is a process of anti-differentiation. The course explores some of the more frequently used trigonometric integrals as well as the trigonometric substitutions useful in integrating certain binomials.
Furthermore, in integration, we have the derivative of a function and we need to find the original function. In order to use the method of Integration by partial fractions, we must first decompose a fractional integral into the sum of simpler fractions. You will learn about partial fraction decomposition, first-order differential equations and how to satisfy initial conditions when solving differential equations. The integration by parts is a technique that is frequently useful for integrating functions that are described by the product of two functions. This course illustrates other integration methods; Integration of inverse trigonometric functions and Integration of hyperbolic functions. You will be able to solve for arc length, the surface of revolution and determine the volume of solid with known cross-section. Calculus can be applied to equations expressed in polar coordinates. These area ranges from finding the area using polar coordinates, finding the polar coordinates of the point with cartesian coordinates and finding the cartesian equation of a curve. The learning content in this course is crucial for students, researchers, engineers, analysts or anyone with an interest in the working knowledge of Integration. So, register for this course and start your next learning.Start Course Now
Methods of Integration
Methods of Integration - Learning Outcomes
Fundamental Theorem of Integral Calculus
Linear Differential Equations
Methods of Integration - Lesson Summary
Integrating Techniques and Definite Integrals
Integrating Techniques and Definite Integrals - Learning Outcomes
Inverse Trigonometric Functions
Applications of Definite Integral
Volume of Solid of Revolution
Integrating Techniques and Definite Integrals - Lesson Summary
Upon the successful completion of this course, you should be able to:
- State Hooke law.
- Identify the application of definite integrals.
- List the methods used to determine the volume of a solid of revolution.
- Explain disk methods, washer method and cylindrical shell method.
- Recall how to calculate compound interest.
- Evaluate the volume of solids with known cross-sections.
- Recall how to find hyperbolic cosine and hyperbolic sine functions.
- Recall how to find the derivative of a function.
- Describe integration using partial fraction decomposition.
- Analyze the method of u-substitution to find the integrals.
- State the rules used in anti - differentiating.
- Distinguish the first and second fundamental theorem of integral calculus.
- List the properties of definite integrals.
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