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Summary Integration Notes: Indefinite & Definite Integrals with Formulas and Solved Examples

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This document contains clear and simple integration notes designed for A/L and university students. It covers both indefinite and definite integrals with step-by-step explanations and solved examples. The notes include important integration formulas, rules, and methods such as power rule, substitution method, and basic integration techniques. It is prepared in an easy-to-understand format to help students quickly revise and improve problem-solving skills. These notes are ideal for exam revision, assignment preparation, and building a strong foundation in calculus. Suitable for beginners as well as advanced learners who want quick and effective revision material.

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Institution
Fifth Year / 11th Grade
Course
BBST

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SIMPLE MATHEMATICS NOTES

1. INDICES (POWERS)

Rules

aᵐ × aⁿ = aᵐ⁺ⁿ

aᵐ ÷ aⁿ = aᵐ⁻ⁿ

(aᵐ)ⁿ = aᵐⁿ

a⁰ = 1

a⁻ⁿ = 1/aⁿ



Examples

2² × 2³

= 2⁵

= 32



x⁵ ÷ x²

= x³



2. SURDS

Rules

√a × √b = √ab

√a / √b = √(a/b)



Examples

√4 × √9

=2×3

=6

, √16

=4



3. ALGEBRAIC IDENTITIES

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

a² - b² = (a+b)(a-b)



Example

(x + 2)²

= x² + 4x + 4



4. FACTORIZATION

Common Factor

6x + 12

= 6(x + 2)



Difference of Squares

x² - 9

= (x + 3)(x - 3)



5. LINEAR EQUATIONS

Example

2x + 5 = 11

2x = 6
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  • calculus integration integral calculus indefini
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