Definite

25
Feb
Pattern – 2 : Indefinite Integration

⋆ Pattern – 2 :

If ∫f(x) dx = F(x) +c, then

∫ f (a + b) dx = \frac{1}{a} F ( ax + b )dx + c  :  a ≠ 0

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Posted in: Pattern – 2 : Indefinite Integration,
Tags: math, pattern, of, dx, maths, 1/a, mathematics, sabiti, ganit, proof, f(ax+b), definition, math maths, formula, any, Definite, integration,
16
Feb
Indefinite Integration

⋆ Pattern – 1

Definite integration never contains any arbitrary constant.

i.e.   If   = F(x) + c, then

=  F(b) – F(a)

Proof :

Now,  dx = F(b) – F(a)

= [ F(b) + c ] – [ F(a) + c ]

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Posted in: Indefinite Integration,
Tags: never, maths, contains, mathematics, arbitrary, proof, constant, definition, pattern, formula, defination, 1, statement, any, indefinite, proofs, Definite, mathematical, integration,