Techniques of Integration — Single-Variable Calculus
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[FUTA, Akure] MTS 102: Introductory Mathematics IIThis 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 IIThis 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
1Introduction
Meaning of integration; classification of integrals - indefinite, definite, proper and improper integrals.
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2Standard Integrals
Integrals involving standard functions - constants, x^n, trigonometric and inverse trigonometric, exponential and logarithmic, hyperbolic and inverse hyperbolic functions.
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3Basic Rules of Integration
Rules of integrating functions involving sums, multiples, etc., of other functions.
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4Change of Variable
How to do a variable substitution in integration; integration by trigonometric substitutions.
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5Functions of a Linear Function
Integrating functions of a linear function.
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6Function-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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7Partial Fractions
Integration of some rational algebraic functions by resolution into partial fractions.
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8Rational Algebraic Functions
Integration of rational algebraic functions not directly resolvable into partial fractions.
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9Trigonometric Functions
Integrals of powers and products of sines and cosines.
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10Integration by Parts
Integrals of products of functions.
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11Special 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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12Special 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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13Reduction Formulas I
Generation and use of reduction formulas for integration by parts.
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14Reduction Formulas II
Generation and use of reduction formulas for integration by parts continued.
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15Some Applications
Some applications of integration - areas, volumes, and an introduction to differential equations.
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