CLEP Calculus: Integral Calculus and Applications
This free online course explains the various methods of integration, as well as applications of the definite integrals.Publisher: ADU
CertificationView course modules
CLEP Calculus: Integral Calculus and Applications is a free online course that has been specifically designed to teach you about the various methods and application 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 constant of integration. The relationship between Riemann Sums and area under a curve will be highlighted in this course. You will also be introduced to the functions of Sigma notation along with its various formulas. When working with a variable number of terms in calculus, it is important to understand the dummy variable and stopping point. The multiple formulas for sums of sequences will also be introduced to you. Did you know that there are three sigma laws? Prepare yourself to learn about their differences, as well as the appropriate use of these laws to simplify calculations. Upon the completion of this course, you will be able to analyze how to get the exact area under a curve.
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 in this course. u-Substitution allows for an immediate reversal of the process of differentiation. You will learn how to find integrals using the u-Substitution method. This course will teach 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. Decomposing a fraction into simpler functions is also imperative in Calculus. Examine how to integrate partial functions. There is a slightly more complicated type of first order differential equation. This course will teach you about separable differential equations. You will also be able to explain the technique of integration by parts.
Furthermore, you will acquire knowledge on integrating inverse trigonometric and natural exponential functions. The relationship between the velocity, along with the position function. You will 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 in this course. The formula for area of region in a plane will also be examined. You will be able to explain the surface of revolution and how to find the arc length. Exponential growth and decay are key concepts in calculus. You will become familiar with their various applications. This course will be of great interest to students, researchers, teachers, and anyone with an interest in integral calculus and applications. So, register for this course and start your next learning journey today.Start Course Now
Definite and Indefinite Integrals
Definite and Indefinite Integrals - Learning Outcomes
Definite and Indefinite Integral
Average Value Function
Definite and Indefinite Integrals - Lesson Summary
Power Rules of Integration
Power Rules of Integration - Learning Outcomes
Power Rules of Integration
Integration by Parts
Power Rules of Integration - Lesson Summary
Velocity and Position Equation
Velocity and Position Equation - Learning Outcomes
Velocity and Position Equation
Area of Region
Exponential Growth and Decay
Velocity and Position Equation - Lesson Summary
Upon the successful completion of this course, you should be able to:
- Explain the concepts of anti-differentiation.
- Distinguish between definite and indefinite integrals.
- State the three sigma laws.
- State the power rule of integration.
- Discuss integration by u-substitution.
- Explain how to integrate natural logarithmic and exponential functions.
- Explain the velocity and position equation.
- State how to find the area above and below the x-axis.
- Discuss the volume of a solid of revolution.
All Alison courses are free to enrol, study and complete. To successfully complete this Certificate course and become an Alison Graduate, you need to achieve 80% or higher in each course assessment. Once you have completed this Certificate course, you have the option to acquire an official Certificate, which is a great way to share your achievement with the world. Your Alison Certificate is:
Ideal for sharing with potential employers - include it in your CV, professional social media profiles and job applications
An indication of your commitment to continuously learn, upskill and achieve high results
An incentive for you to continue empowering yourself through lifelong learning
Alison offers 3 types of Certificates for completed Certificate courses:
Digital Certificate - a downloadable Certificate in PDF format, immediately available to you when you complete your purchase
Certificate - a physical version of your officially branded and security-marked Certificate, posted to you with FREE shipping
Framed Certificate - a physical version of your officially branded and security-marked Certificate in a stylish frame, posted to you with FREE shipping
All Certificates are available to purchase through the Alison Shop. For more information on purchasing Alison Certificates, please visit our FAQs. If you decide not to purchase your Alison Certificate, you can still demonstrate your achievement by sharing your Learner Record or Learner Achievement Verification, both of which are accessible from your Dashboard. For more details on our Certificate pricing, please visit our Pricing Page.