Mathematical Proofs

Parin Sir > Mathematical Proofs

Feb

Pattern – 7 :

$\int_{a}^{a}f\left(x\right)dx=0$

Proof :

Let ∫f(x) dx = F(x) + c

Now,

$... </p> <div class=$

Posted in: Pattern – 7 : Definite integration,

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

Feb

⋆ Pattern – 6 :

$\int_{a}^{b}f\left(x\right)\ dx=\ \int_{a}^{b}f\left(a+b-x\right)dx$
…

Posted in: Pattern – 6 : Definite integration,

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

Feb

If a < c < b, then $\int_{a}^{b}f\left(x\right)dx$ = $\ \int_{a}^{c}f\left(x\right)dx+\&... </p> <div class=$

Posted in: Pattern – 5 : Definite integration,

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

Feb

$\int_{a}^{b}f\left[g\left(x\right)\right]g^\prime\left(x\right... </p> <div class=$

Posted in: Pattern – 4 : Definite integration,

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

Feb

⋆ Pattern – 3

$\int_{a}^{b}f\left(x\right)\ dx=\ -\ \int_{b}^{a}f\left(x\right)\ dx$

Posted in: Pattern – 3 : Definite integration,

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

Feb

⋆ Pattern – 2

The value of a definite integral does not change with change of variable of integration provided the limits of integration remains the same.

i.e. $\int_{a}^{b}f\left(x\right)\&spac... </p> <div class=$

Posted in: Pattern – 2 : Definite integration,

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