lightbulb Key Concepts

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1. Definition

Integration is the process of finding the anti-derivative. It represents the area under a curve.

2. Basic Integrals

• ∫ xⁿ dx = (xⁿ⁺¹) / (n+1) + C
• ∫ (1/x) dx = log |x| + C
• ∫ eˣ dx = eˣ + C
• ∫ sin x dx = -cos x + C
• ∫ cos x dx = sin x + C

3. Methods of Integration

• Substitution: Replace a part of the integrand with a new variable 'u'.
• By Parts: ∫ uv dx = u ∫ v dx - ∫ [u' ∫ v dx] dx
• Definite Integral: Calculates the net area between two limits [a, b].