Integral Calculus & The Fundamental Theorem

Overview

Master the essential concepts of integral calculus and discover the fundamental theorem that revolutionizes mathematical analysis. In this comprehensive course, you'll develop expertise in calculating definite and indefinite integrals, apply integration techniques to real-world problems, and understand the profound connection between differentiation and integration. You'll learn systematic approaches to integration by partial fractions, integration by parts, and trigonometric function integration. Explore practical applications including area calculations, volume of solids of revolution, and curve length determination. The course culminates with the fundamental theorem of calculus, revealing how differentiation and integration form two sides of the same mathematical coin. By completing this course, you'll gain competency in identifying relevant integration techniques, executing calculations accurately, and understanding differential equations as tools for describing system dynamics. Whether you're pursuing data science, engineering, physics, or advanced analytics, these foundational calculus skills are essential for modeling complex phenomena and solving quantitative challenges. You'll develop the analytical thinking and mathematical precision needed to tackle sophisticated problems across multiple disciplines.

Syllabus

Definite and Indefinite Integrals and Integration by Partial Fractions

You will be introduced to definite and indefinite integrals this week and will learn how to simplify complex expressions using partial fractions. You are provided with practice integration techniques and will explore how these tools are used in real-world data analysis.

Integration by Parts and Applications of integration including areas, volume of revolutions and length of curve

Integration by parts is introduced this week alongside applications such as calculating areas, volumes, and curve lengths. You can work through examples and practice problems to understand how integration supports modelling and analysis.

The Fundamental Theorem of Calculus

This week we will explore Fundamental Theorem of Calculus, linking differentiation and integration. You are going to study both parts of the theorem and apply it to evaluate definite integrals and understand accumulation.