INTEGRATION : LSUS
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. ∫x5/2 dx 3.∫ 4/ x5 dx 4.∫ √x8 5.∫ (7x4 + 2) dx 6.∫(x5 + 2x4 – x3 + 6) dx
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- PROJECTILES: MOTION UNDER GRAVITY IN TWO DIMENSION, DERIVATION AND APPLICATION OF EQUATION INVOLVING GREATEST HEIGHT, TIME OF FLIGHT AND RANGE
- BINOMIAL EXPANSION: PASCAL TRIANGLE, BINOMIAL THEOREM OF NEGATIVE, POSITIVE AND FRACTIONAL POWER
- MECHANICS (VECTOR GEOMETRY)
- MECHANICS: VECTORS OR CROSS PRODUCT ON TWO OR THREE DIMENSION, CROSS PRODUCT OF TWO VECTORS AND APPLICATION OF CROSS PRODUCT.
- INTEGRATION
- INTEGRATION (INDEFINITE INTEGRAL, DEFINITE INTEGRAL AND AREA UNDER CURVE
- APPLICATION OF INTEGRATION II: SOLID REVOLUTION AND TRAPEZOIDAL RULE
- REGRESSION LINE AND CORRELATION COEFFICIENT SCATTER DIAGRAM
- Chapters 8
- Category SSS2
- Author ClassNotes Edu
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