Definite

01
Mar
Pattern – 31 : Definite integration

Pattern – 31 :

If  f^2 (x) and g^2(x) are integrable on the interval [a, b], then prove tha…

Share
Posted in: Pattern – 31 : Definite integration,
Tags: integration, math, pattern, of, sabiti, maths, mathematics, ganit, proof, definition, formula, any, Definite,
01
Mar
Pattern – 30 : Definite integration

⋆ Pattern – 30 :

If m is the least value (global minimum) and M is greatest value (global maximum) of f(x) for  ∀ x ∈ [a, b]

i.e.    m  ≤   f(x)  ≤   M  ;  x  [a, b],

then prove that

m (b – a) ≤ 

Share
Posted in: Pattern – 30 : Definite integration,
Tags: mathematics, ganit, proof, definition, formula, any, Definite, integration, math, pattern, of, sabiti, maths,
01
Mar
Pattern – 29 : Definite integration

⋆ Pattern – 29

f is continuous on [a, b] and | f(x) | ≤ k, ∀ x ∈ [a, b], then  \left|\int_{a}^{b}f\left(x\right)dx\right| ≤ k (b-a…

Share
Posted in: Pattern – 29 : Definite integration,
Tags: definition, formula, any, Definite, integration, math, pattern, of, sabiti, maths, mathematics, ganit, proof,
01
Mar
Pattern – 28 : Definite integration

⋆ Pattern – 28

f is continuous on [a, b], then \left| \left|\ \int_{a}^{b}f\left(x\right)\ dx\ \right|

Share
Posted in: Pattern – 28 : Definite integration,
Tags: integration, math, pattern, of, sabiti, maths, mathematics, ganit, proof, definition, formula, any, Definite,