INTEGRATION

FURTHER MATHEMATICS SSS2 THIRD TERM

WEEK 7

INTEGRATION

Content

Integration: This is defined as anti-differentiation. Suppose, y = x³ + 2x, the first derivative is

 3x² + 2. (dy/dx = 3x² + 2)

then the antiderivative of  3x² + 2 = x³ + 2x

 Thus, integration is the reverse process of differentiation and is denoted by the symbol ∫.

If  dy/dx = xⁿ , then  ∫ dy/dx = xⁿ⁺¹   + C

n + 1           (n ≠ -1)

where c is the arbitrary constant.

 

INDEFINITE INTEGRAL CONCEPTS

General Concept

Example:  Evaluate the following integrals:
       1. ∫x² dx      2. ∫x^5/2 dx     3.∫ 4/ x5 dx      4.∫ √x⁸…