Integration

Basic Integration

• Understand integration as the reverse process of differentiation.
• Know how to perform indefinite integration of any given function.
• Be aware of the basic rules of integration, including power rule, constant rule and sum rule.

Integration Techniques

• Familiarise with and apply the substitution method for integration.
• Recognise when the integration by parts method should be applied and implement it proficiently.
• Be competent in executing the methods of partial fractions to perform non-elementary integrations.
• Understand the trigonometric substitution method, and recognise when and how to apply it.

Definite Integrals

• Understand and become proficient in calculating definite integrals.
• Understand the concept of area under a curve and be able to use definite integrals to calculate it.
• Be comfortable evaluating improper integrals by taking limits.

Applications of Integration

• Understand and apply the principles of integration to solve problems involving area between curves.
• Familiarise with and apply integration to calculate volumes of revolution.
• Understand and be able to apply integration in various physical contexts, such as calculating distances from velocity functions or moments in mechanics.

Numerical Integration

• Familiarise with and understand the uses of numerical integration techniques, such as the trapezium rule and Simpson’s rule.
• Be proficient in applying these techniques to approximate integrals when an analytical approach is not feasible.

Integration and Differential Equations

• Understand the relationship between integration and differential equations.
• Be able to solve and interpret the solutions of first-order differential equations using integration.