Integration

Integration

Fundamental Concepts

• Understand the concept of integration as the reverse process of differentiation.
• Familiarise yourself with the symbols and notations used in integration. The integral sign (∫) denotes integration, while ‘dx’ represents a small change in x.

Indefinite and Definite Integrals

• Distinguish between indefinite and definite integrals. An indefinite integral, also known as an antiderivative, lacks defined limits, whereas a definite integral calculates the signed area under a curve between two given points.
• Understand that constant of integration (C) is an important element of indefinite integrals, representing the family of possible solutions.

Basic Integration Rules

• Master the basic rules of integration, which include power rule, sum rule, constant multiple rule, exponential rule, and trigonometric rules.

Integration Techniques

• Familiarise yourself with integration by substitution, a technique used to simplify complex integrals making them easier to calculate.
• Learn to use integration by parts, a method based on the product rule of differentiation.

Definite Integrals and Area under the Curve

• Learn how to apply definite integrals to calculate the total area under a curve. Remember that the area below the x-axis is taken as negative.

Applications of Integration

• Understand the real-world applications of integration, including finding areas between curves, volumes of solid revolution, and solving physical problems in kinematics and dynamics.

Always supplement these guidelines with detailed notes, textbooks, and work through plenty of practice problems. This process will aid in understanding and recalling these concepts ready for exams.