Techniques of Integration — Single-Variable Calculus

With the basics in place, this course moves into practical methods of integration, such as substitution, integration by parts, and partial fractions. You’ll learn when and how to apply each technique, and how to recognize integrable forms efficiently. We also cover integrals involving trigonometric identities and improper integrals. It’s a hands-on course that gives you the tools to handle a wide range of integral expressions confidently.

$ 8.58

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Enrolment valid for 12 months
This course is also part of the following learning tracks. You may join a track to gain comprehensive knowledge across related courses.
[FUTA, Akure] MTS 102: Introductory Mathematics II
[FUTA, Akure] MTS 102: Introductory Mathematics II
This learning track is structured for first-year students at the Federal University of Technology, Akure (FUTA) and mirrors the standard second-semester coverage of elementary calculus. It begins with single-variable functions and their graphs, then walks learners through limits, continuity, differentiation techniques, and curve sketching—just as covered in the official MTS 102 outline. You’ll also explore anti-derivatives and integration, learning both the techniques and how to apply them to solve practical problems in science and engineering contexts. Everything is broken down into short, focused video lessons that keep things clear and manageable, especially for students who might be engaging this content for the first time. If you're not a FUTA student but need to build a solid foundation in these same topics, this track can serve you just as well. The structure and explanations are universal, ensuring that learners with similar academic goals can benefit fully.

This learning track is structured for first-year students at the Federal University of Technology, Akure (FUTA) and mirrors the standard second-semester coverage of elementary calculus. It begins with single-variable functions and their graphs, then walks learners through limits, continuity, differentiation techniques, and curve sketching—just as covered in the official MTS 102 outline. You’ll also explore anti-derivatives and integration, learning both the techniques and how to apply them to solve practical problems in science and engineering contexts. Everything is broken down into short, focused video lessons that keep things clear and manageable, especially for students who might be engaging this content for the first time. If you're not a FUTA student but need to build a solid foundation in these same topics, this track can serve you just as well. The structure and explanations are universal, ensuring that learners with similar academic goals can benefit fully.

[UNILAG, Akoka] MTH 102: Elementary Mathematics II
[UNILAG, Akoka] MTH 102: Elementary Mathematics II
This learning track is designed to guide first-year students at the University of Lagos through key concepts in calculus, beginning with the fundamentals of single-variable functions and their graphs. It builds gradually into the core topics of limits, continuity, and differentiability, with each course tailored to simplify these foundational ideas for early learners. The focus is not just on theory but also on building the skill to solve problems confidently, especially those typically encountered in university-level exams. You’ll move from understanding the concept of a limit to mastering how derivatives work and how to apply them to sketch curves and analyze function behavior. Although built for UNILAG students, this track is suitable for anyone looking to strengthen their understanding of introductory calculus at the university level. Whether you're preparing for school assessments or seeking a solid refresher, this track will help you follow a structured path.

This learning track is designed to guide first-year students at the University of Lagos through key concepts in calculus, beginning with the fundamentals of single-variable functions and their graphs. It builds gradually into the core topics of limits, continuity, and differentiability, with each course tailored to simplify these foundational ideas for early learners. The focus is not just on theory but also on building the skill to solve problems confidently, especially those typically encountered in university-level exams. You’ll move from understanding the concept of a limit to mastering how derivatives work and how to apply them to sketch curves and analyze function behavior. Although built for UNILAG students, this track is suitable for anyone looking to strengthen their understanding of introductory calculus at the university level. Whether you're preparing for school assessments or seeking a solid refresher, this track will help you follow a structured path.

Course Chapters

1
Introduction

Meaning of integration; classification of integrals - indefinite, definite, proper and improper integrals.

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2
Standard Integrals

Integrals involving standard functions - constants, x^n, trigonometric and inverse trigonometric, exponential and logarithmic, hyperbolic and inverse hyperbolic functions.

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3
Basic Rules of Integration

Rules of integrating functions involving sums, multiples, etc., of other functions.

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4
Change of Variable

How to do a variable substitution in integration; integration by trigonometric substitutions.

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5
Functions of a Linear Function

Integrating functions of a linear function.

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6
Function-Derivative Forms

Integrating functions in the form of the product of some function and its derivative, or the quotient of the derivative of some function and the function.

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7
Partial Fractions

Integration of some rational algebraic functions by resolution into partial fractions.

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8
Rational Algebraic Functions

Integration of rational algebraic functions not directly resolvable into partial fractions.

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9
Trigonometric Functions

Integrals of powers and products of sines and cosines.

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10
Integration by Parts

Integrals of products of functions.

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11
Special Forms I

Integration of functions of the form 1/f, where f is a quadratic function or square root of a quadratic function.

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12
Special Forms II

Integration of functions of the form 1/f, where f involves sines and cosines - both of first or second degree.

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13
Reduction Formulas I

Generation and use of reduction formulas for integration by parts.

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14
Reduction Formulas II

Generation and use of reduction formulas for integration by parts continued.

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15
Some Applications

Some applications of integration - areas, volumes, and an introduction to differential equations.

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