Fundamentals and Techniques of Integration - Calculus (Undergraduate Foundation)

Integration is the essential tool for summing tiny changes into whole totals. This course covers the reversal of differentiation to find areas, volumes, and precise solutions. You will learn how to handle indefinite integrals and master core methods like substitution and integration by parts. The curriculum also includes reduction formulae to simplify repeated, complex calculations. Mastering these techniques is the first step toward solving the advanced problems found in engineering and the physical sciences. Engineers and scientists use these methods to design structures, predict natural events, and build hardware. Knowledge of integration allows you to calculate the work done by varying forces or the exact flow of fluids in a system. If you plan to work in technical fields or handle data-driven projects, these calculations are unavoidable. This course provides the practical math needed to turn abstract formulas into real-world applications and professional results. After completing these modules, you will correctly identify and apply the right integration technique for any given problem. You will solve indefinite integrals using standard rules and perform variable changes through the substitution method. You will also manage products of functions using integration by parts and apply reduction formulae to streamline long processes. These skills prepare you to tackle the differential equations required in higher university years and professional licensing exams. This course is for undergraduate students in engineering, mathematics, and the sciences seeking a firm foundation in calculus. It also serves secondary school leavers who want to prepare for the rigours of university-level technical courses. Even for those outside of science tracks, the logic and step-by-step methods taught here improve general analytical thinking and problem-solving. This training ensures you meet the international standards expected in any modern technical career.

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.
AMS 102: Basic Mathematics
AMS 102: Basic Mathematics
Management and administration require precise numerical logic for decision-making. This track follows the official NUC CCMAS syllabus for AMS 102, covering real numbers, set theory, and complex systems. You will master algebraic operations, permutations, and combinations alongside the foundations of trigonometry and calculus. It provides the mathematical tools to model financial trends, handle business data, and solve optimisation problems in corporate settings. This programme is built for first-year university students in Accounting, Business Administration, Banking, Finance, and Public Administration. It also serves secondary school leavers preparing for management degrees and professionals needing a refresher on business mathematics. It is suitable for anyone moving into roles that demand accurate quantitative analysis and logical deduction. You will gain the ability to simplify complex business formulas, calculate probabilities for risk assessment, and find the exact points where profits are highest. You will be able to handle sequences for interest calculations and use differentiation to manage production costs. Completing this track ensures success in university examinations and builds the analytical strength required for careers in financial analysis, auditing, and strategic management.

Management and administration require precise numerical logic for decision-making. This track follows the official NUC CCMAS syllabus for AMS 102, covering real numbers, set theory, and complex systems. You will master algebraic operations, permutations, and combinations alongside the foundations of trigonometry and calculus. It provides the mathematical tools to model financial trends, handle business data, and solve optimisation problems in corporate settings. This programme is built for first-year university students in Accounting, Business Administration, Banking, Finance, and Public Administration. It also serves secondary school leavers preparing for management degrees and professionals needing a refresher on business mathematics. It is suitable for anyone moving into roles that demand accurate quantitative analysis and logical deduction. You will gain the ability to simplify complex business formulas, calculate probabilities for risk assessment, and find the exact points where profits are highest. You will be able to handle sequences for interest calculations and use differentiation to manage production costs. Completing this track ensures success in university examinations and builds the analytical strength required for careers in financial analysis, auditing, and strategic management.

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MTH 102: Elementary Mathematics II - Calculus
MTH 102: Elementary Mathematics II - Calculus
Calculus is the mathematical tool for measuring change and finding the best results in any system. This track follows the official NUC CCMAS MTH 102 curriculum to teach you how functions behave, how to calculate exact rates of change, and how to sum up tiny movements to find total areas or volumes. You will move from basic limits to complex integration techniques used to solve practical problems in the physical world. This track is for first-year university students in engineering, science, and economics departments across Nigeria. It also serves secondary school leavers preparing for technical degrees or university entrance exams. Anyone needing to build a strong foundation in mathematical logic for data analysis or professional licensing will find these lessons essential. After finishing this programme, you will calculate derivatives using first principles and shortcuts, find turning points for optimisation, and solve definite integrals for land measurement or tank design. You will use the trapezium and Simpson's rules to handle experimental data accurately. These skills ensure you pass your university exams and excel in technical careers like civil engineering, physics research, or financial forecasting.

Calculus is the mathematical tool for measuring change and finding the best results in any system. This track follows the official NUC CCMAS MTH 102 curriculum to teach you how functions behave, how to calculate exact rates of change, and how to sum up tiny movements to find total areas or volumes. You will move from basic limits to complex integration techniques used to solve practical problems in the physical world. This track is for first-year university students in engineering, science, and economics departments across Nigeria. It also serves secondary school leavers preparing for technical degrees or university entrance exams. Anyone needing to build a strong foundation in mathematical logic for data analysis or professional licensing will find these lessons essential. After finishing this programme, you will calculate derivatives using first principles and shortcuts, find turning points for optimisation, and solve definite integrals for land measurement or tank design. You will use the trapezium and Simpson's rules to handle experimental data accurately. These skills ensure you pass your university exams and excel in technical careers like civil engineering, physics research, or financial forecasting.

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Course Chapters

1. Introduction
4
3
Integration is the process of reversing differentiation to find the original function or total quantities. This chapter explains the core concept of the anti-derivative and the formal notation used in all calculus studies. It provides the logical starting point for summing tiny changes into whole totals. You will understand the anti-derivative concept; master indefinite integral notation; and apply the basic power rule for integration.
Concept Overviews
4 Lessons
Problem Walkthroughs
3 Lessons
2. Algebraic Integration
4
3
Algebraic integration handles polynomials and terms with complex indices. This chapter expands basic rules to manage sums, differences, and terms in the denominator or under square roots. You will also learn the vital role of the constant of integration in defining specific solutions. You will integrate multi-term polynomials; manage negative and fractional indices; and calculate the constant of integration from specific coordinates.
Concept Overviews
4 Lessons
Problem Walkthroughs
3 Lessons
3. Transcendental Functions
4
3
Transcendental functions include exponentials, logarithms, and trigonometric expressions common in physics and electronics. This chapter provides the standard results for integrating these non-algebraic terms. You will also learn to use identities to prepare complex trigonometric terms for integration. You will integrate exponential and logarithmic functions; master basic trigonometric integrals; and use identities to simplify powers of sine and cosine.
Concept Overviews
4 Lessons
Problem Walkthroughs
3 Lessons
4. Substitution Method
4
3
The substitution method simplifies complex integrals by changing the variable to a simpler form. This technique is used for composite functions where one part of the expression is the derivative of another. Mastering this method is critical for solving high-level calculus problems. You will master the change of variable process; apply linear and non-linear substitutions; and handle integrals involving square roots and radicals.
Concept Overviews
4 Lessons
Problem Walkthroughs
3 Lessons
5. Integration by Parts
3
3
Integration by parts is the method used to integrate the product of two different functions. It is the integral version of the product rule from differentiation and follows a specific priority order for selection. This technique is essential for functions involving combinations of algebra, logs, and exponentials. You will master the product reversal formula; apply the LIATE priority rule; and solve integrals requiring repeated applications of the parts method.
Concept Overviews
3 Lessons
Problem Walkthroughs
3 Lessons
6. Partial Fractions
5
3
Partial fraction decomposition turns complex rational functions into sums of simpler, integrable fractions. This chapter covers the different algebraic cases required to handle linear, repeated, and quadratic factors in the denominator. This method is a standard requirement for solving engineering transfer functions. You will decompose rational functions into partial fractions; integrate terms with linear and repeated factors; and use inverse trigonometric results for quadratic factors.
Concept Overviews
5 Lessons
Problem Walkthroughs
3 Lessons
7. Reduction Formulae
3
3
Reduction formulae provide a systematic way to integrate high powers of functions by relating them to lower powers. This chapter is essential for simplifying long, repetitive calculations involving trigonometric and exponential functions. Mastering these formulas allows you to solve advanced problems with speed and precision. You will understand the logic of recursive integration; apply reduction formulae to trigonometric powers; and simplify polynomial-exponential products.
Concept Overviews
3 Lessons
Problem Walkthroughs
3 Lessons
8. Conclusion
1
The conclusion summarises all integration techniques covered in the course. It serves as a review to ensure you can independently select the most efficient method for any given function. This final stage prepares you for the transition to definite integrals and their applications. You will review all integration methods; identify the best technique for different function types; and confirm your readiness for advanced calculus topics.
Concept Overviews
1 Lesson