Integration Formulas and Techniques for A-Level Mathematics

This page provides a comprehensive overview of integration techniques and formulas essential for A-level Maths Integration. It covers various aspects of integration, from basic formulas to advanced problem-solving strategies.

The page begins with a set of trigonometric integration formulas not typically included in standard formula books. These formulas are crucial for solving complex trigonometric integrals.

Highlight: Key trigonometric integration formulas include ∫secx dx = tan x + c and ∫cosecx dx = -cot x + c.

The guide then moves on to integration formulas for sine and cosine functions raised to various powers, as well as exponential and logarithmic functions.

Example: ∫sin^k x dx = -1/k cos^k x + c and ∫e^kx dx = 1/k e^kx + c

The page also covers integration techniques such as:

1. Integration by Substitution: This method is explained with step-by-step instructions and examples. The guide emphasizes the importance of choosing the correct substitution, usually the expression inside brackets.

Vocabulary: Substitution in integration involves replacing a complex expression with a simpler variable to make the integral easier to solve.

2. Reverse Chain Rule: This technique is applicable to linear equations and involves raising the power by 1 and multiplying by the reciprocal.

3. Integration by Parts: The formula uv - ∫v du is introduced, along with guidance on when to use this method, typically for products of two or more functions.

Definition: Integration by parts is a technique used to integrate products of functions by transforming them into simpler integrals.

4. Integrating Using Trigonometric Identities: The guide provides a list of trigonometric identities not typically given in exams, which are useful for simplifying complex trigonometric integrals.

5. Integrating Partial Fractions: This section explains how to handle integrals where substitution may not work or when dealing with complex rational functions.

The page concludes with instructions on solving definite integrals, emphasizing the importance of applying the given bounds to the final answer.

Quote: "When Solving integrals you are given 2 numbers... You apply these numbers at the end."

This comprehensive guide serves as an excellent resource for students preparing for A-level Maths Integration exams, providing a wealth of formulas, techniques, and problem-solving strategies.