formula

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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Tags: formula, any, Definite, integration, math, pattern, of, dx, maths, 1/a, mathematics, sabiti, ganit, proof, f(ax+b), definition, math maths,
20
Feb
Pattern - 36 of Indefinite Integration

Pattern 36 :

\ I_n=\ \int\left(\log{x}\right)^n\ dx, then

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Tags: pattern, sabiti, maths, formula,
20
Feb
Pattern - 35 of Indefinite Integration

⋆ Pattern – 35

I_n=\ \int x^n\ e^{ax}\ dx

∴ 

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Tags: maths, formula, pattern, sabiti,
20
Feb
Pattern - 33 of Indefinite Integration

⋆ Pattern – 33

I_n=\ \int x^n sin\ mx\ dx, then I_n

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Tags: formula, pattern, sabiti, maths,
20
Feb
Pattern - 32 of Indefinite Integration

⋆ Pattern – 32

I_n=\cos^n{x} dx

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Tags: maths, formula, pattern, sabiti,
20
Feb
Pattern - 31 of Indefinite Integration

⋆ Pattern – 31

I_n=\ \int\sin^n{x}\ dx, then

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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,