Mathematical Proofs

Parin Sir > Mathematical Proofs

Mar

Pattern – 27 : Definite integration

⋆ Pattern – 27

∀ x ∈ [ a, b ], g(x) ≤ f(x) ≤ h(x), then $\int_{a}^{b}g\left(x\right) dx$ ≤

Posted in: Pattern – 27 : Definite integration,

Tags: of, sabiti, maths, mathematics, ganit, proof, definition, formula, any, Definite, integration, math, pattern,

Mar

Pattern – 26 : Definite integration

⋆ Pattern – 26

Method to express infinite series as define integrals.

Step – 1 :-

Find $T_r=r^{th}$ term of infinite series.

Step – 2 :-

Taking common …

Posted in: Pattern – 26 : Definite integration,

Tags: ganit, proof, definition, formula, any, Definite, integration, math, pattern, of, sabiti, maths, mathematics,

Mar

Pattern – 25 : Definite integration

⋆ Pattern – 25 (Mean value theorem)

If f is a continuous function on [a, b], then there exists c ∈ (a, b) such that

f(c) = $\frac{1}{b\ -\ a}\int_{a}^{b}f\ \left(t\rig... </p> <div class=$

Posted in: Pattern – 25 : Definite integration,

Tags: any, Definite, integration, math, pattern, of, sabiti, maths, mathematics, ganit, proof, definition, formula,

Mar

Pattern – 24 : Definite integration

⋆ Pattern – 24(Leibnitz’s Theorem)

If f is a continuous function on [a, b] and u(x) and v(x) are differentiable functions of x whose values lie in [a, b], then

$\frac{d}{dx}\left\{\int_{u(x)}^{v(x)}f... </p> <div class=$

Posted in: Pattern – 24 : Definite integration,

Tags: math, pattern, of, sabiti, maths, mathematics, ganit, proof, definition, formula, any, Definite, integration,

Mar

Pattern – 23 : Definite integration

⋆ Pattern – 23

If f(t) is an odd function then

$g\left(x\right)\ =\ \int_{0}^{x}f\ \left(t\right)dt$

Posted in: Pattern – 23 : Definite integration,

Tags: ganit, proof, definition, formula, any, Definite, integration, math, pattern, of, sabiti, maths, mathematics,

Mar

Pattern – 22 : Definite integration

⋆ Pattern – 22

If f(t) is an even function then

$g\left(x\right)\ =\ \int_{0}^{x}f\ \left(t\right)dt$

Posted in: Pattern – 22 : Definite integration,

Tags: formula, any, Definite, integration, math, pattern, of, sabiti, maths, mathematics, ganit, proof, definition,

Mar

Pattern – 21 : Definite integration

⋆ Pattern – 21

If f(t) is an odd function, then

$\emptyset\left(x\right)\$ = $\ \int_{a}^{x}... </p> <div class=$

Posted in: Pattern – 21 : Definite integration,

Tags: integration, math, pattern, of, sabiti, maths, mathematics, ganit, proof, definition, formula, any, Definite,

Feb

Pattern – 20 : Definite integration

⋆ Pattern – 20 :

If f(x) is an odd periodic defined on interval $\left[-\frac{T}{2},\ \ \frac{T}{2}\right]$ , whe…

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Tags: mathematics, ganit, proof, definition, formula, any, Definite, integration, math, pattern, of, sabiti, maths,

Feb

Pattern – 19 : Definite integration

⋆ Pattern – 19 ( Odd Function )

If f is an odd periodic function with principal period T, then is an even periodic function with principal period T.

Proof :

Let, g(x) – $\int_{a}^{x}f\left(t\ri... </p> <div class=$

Posted in: Pattern – 19 : Definite integration,

Tags: definition, formula, any, Definite, integration, math, pattern, of, sabiti, maths, mathematics, ganit, proof,

Feb

Pattern – 18 : Definite integration

⋆ Pattern – 18(Even – off function) :

If f is a periodic function with principal period T, then

$\int_{0}^{T}f\left(t\right)dt$ =

Posted in: Pattern – 18 : Definite integration,

Tags: integration, math, pattern, of, sabiti, maths, mathematics, ganit, proof, definition, formula, any, Definite,