Free online courseMath Fundamentals Integrals
Duration of the online course: 1 hours and 57 minutes
5
(1)
Master integral calculus with our free online course on Math Fundamentals. Learn about primitive functions, polynomial primitives, integration techniques, and area calculations.
In this free course, learn about
- Basic Antiderivatives and Polynomial Integration
- Substitution Basics and Pseudo-Immediate Primitives
- Trigonometric Integrals and Arctangent Techniques
- Rational Functions and Partial Fractions
- Areas Under Curves and Between Functions
- Advanced Integration Techniques and Applications
Course Description
Embark on an enlightening journey through the intricate world of integrals with the course "Math Fundamentals Integrals" offered. Designed to provide a solid grounding in integral calculus, this course spans a duration of 1 hour and 57 minutes, offering an engaging introduction to the essentials of integration. While the course has not yet received any reviews, it stands as a valuable resource for anyone seeking to enhance their mathematical foundation.
This course is categorized under Basic Studies and falls within the subcategory of Geometry, making it an ideal choice for students and enthusiasts eager to delve into the principles of integration. The course content comprehensively covers a multitude of subjects, ensuring a well-rounded understanding of integrals and their applications.
Beginning with the rudimentary concept of primitive functions of the powers, the course progresses to explore the linearity and primitives of polynomials. You will also delve deeply into the arctangent function and its derivative, which form the basis for understanding more complex integral calculations.
As you advance, you will encounter pseudo-immediate primitives and partake in three progressive sessions on integration, each building upon the last. The segment on primitives of trigonometric functions opens a gateway to the complexities involved in trigonometric integration.
Next, you’ll learn about completing the square, which is a crucial technique in simplifying and solving integral problems. Subjects on arctangent primitives and the primitives of rational functions (in two dedicated sessions) further cement your knowledge base.
Calculation of areas, an essential practical application of integration, is thoroughly addressed through several focused lessons. You will learn to calculate areas enclosed by a curve, tackle area calculations involving a single function and two functions, and even explore more complex area calculations across two advanced sessions.
The course also delves into the change of variable technique, and the powerful method of integration by parts. These topics are essential for simplifying otherwise daunting integral problems.
Concluding with practical applications of integrals, the course brings theoretical knowledge into a practical perspective, showcasing how integral calculus is applied in various real-world scenarios.
Regardless of your current level of expertise, "Math Fundamentals Integrals" serves as an exceptional stepping stone into the realm of integral calculus. With logically structured content and a focus on foundational principles, this course is perfect for anyone looking to enhance their mathematical acumen in the field of geometry and integration.
Course content
- Video class: Primitive functions of the powers | 1/20 | UPV 07m
- Exercise: Which of the following is the proper form of the antiderivative for the function x raised to a rational exponent, such as x^(n/m)?
- Video class: Linearity and primitive of polynomials | 2/20 | UPV 05m
- Exercise: Given the polynomial function P(x) = 4x^3 - 5x + 1, what is the antiderivative, or the integral, of this function?
- Video class: Arctangent function and its derivative | 3/20 | UPV 04m
- Exercise: What is the integral of the function 1 / (1 + x²) with respect to x?
- Video class: Pseudo-inmediate primitives | 4/20 | UPV 06m
- Exercise: What is the integral of f(x) raised to 'a', given f(x) is a differentiable function?
- Video class: Integration I | 5/20 | UPV 03m
- Exercise: Consider the integral \( \int (3x^2 + x) \cdot (x^3 + x + 1)^{\frac{1}{2}} \, dx \). What is the pseudo-immediate primitive of this integral?
- Video class: Integration II | 6/20 | UPV 04m
- Exercise: Evaluate the integral \( \int \frac{3x}{x^2 + 2} \, dx \). Which method is most suitable for solving it?
- Video class: Integration III | 7/20 | UPV 03m
- Exercise: Consider the integral of the function f(x) = x / (x^4 + 1). Which of the following substitutions would be most appropriate to simplify and solve this integral using the technique of substitution?
- Video class: Primitives of trigonometric functions | 8/20 | UPV 05m
- Exercise: What is the antiderivative of the sine function?
- Video class: Completing the square | 9/20 | UPV 07m
- Exercise: For the quadratic function f(x) = 2x^2 + 8x + 6, what is the vertex form of this parabola after completing the square?
- Video class: Arctangent primitives | 10/20 | UPV 05m
- Exercise: What is the first step when integrating an arctangent type integral where the denominator is an irreducible second-degree polynomial?
- Video class: Primitives of rational functions I | 11/20 | UPV 06m
- Exercise: Which of the following represents a correct primitive (antiderivative) of the function f(x) = 1/(x^2 - 1)?
- Video class: Primitives of rational functions II | 12/20 | UPV 07m
- Exercise: Which integral technique is primarily used to decompose a rational function into simpler fractions for easier integration?
- Video class: Areas enclosed by a curve | 13/20 | UPV 05m
- Exercise: Given the function f(x) is defined and positive over the interval [a, b], and F(x) is a primitive of f(x), what does the definite integral of f(x) from a to b represent?
- Video class: Area calculation (Single function) | 14/20 | UPV 06m
- Exercise: Consider a function g(x) that is positive between x = 0 and x = 3 and negative between x = 3 and x = 5. What is the correct way to calculate the total area between the graph of g(x) and the x-axis over the interval [0, 5]?
- Video class: Area calculation (Two functions) | 15/20 | UPV 07m
- Exercise: Consider two continuous functions, f(x) and g(x), where f(x) is above g(x) on the interval [a, b] and g(x) is above f(x) on the interval [b, c]. What is the correct way to calculate the area enclosed between these two functions from a to c?
- Video class: Area calculation (Complex I) | 16/20 | UPV 05m
- Exercise: What is the total area of the region bounded by the lines x + y = 2, y = 2, and the parabola y = x² that includes the point (0, 1)?
- Video class: Area calculation (Complex II) | 17/20 | UPV 04m
- Exercise: Consider the region bounded by the parabola y = x^2, the line y = 2, and the line x + y = 2. Calculate the area of this region.
- Video class: Change of variable | 18/20 | UPV 07m
- Exercise: What is the primary purpose of using the change of variable technique in integral calculus?
- Video class: Integration by parts | 19/20 | UPV 06m
- Exercise: When using integration by parts for the integral \( \int x \cdot e^x \, dx \), which functions should be chosen as 'u' and 'dv'?
- Video class: Practical applications | 20/20 | UPV 08m
- Exercise: What is a key technique used to simplify the integral of compositions like the sine of the natural logarithm of x?
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1 hours and 57 minutes of online video course
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