INTEGRATION
This is the inverse process of differentiation, if the differentiation of F(x) with respect to x be f(x) then the integration of f(x) with respect to x is F(x) i.e.,
But the derivative of a constant term is zero then
The process of finding the integral of a function is said to be integration and the function which is to be integrated is known as integrand.
Definite Integrals:
The definite integral is denoted by
and is read as “the integral of the function f(x) w.r.t. ‘x’ from x = a to x = b”,
Property I.
(i.e., the value of a definite integral depends on the limits and not on the variable of integration)
Property II.
(i.e., the interchange of limits changes the sign of the integral)
Property III.
Property IV.
Property V.
Property VI.
Wallis formula:
Case-I. When n is odd,
Reduction formula for
Here a generalized formula
When m and n both are even K = π/2
Otherwise K =1,
Leibnitz rule of Differentiation:
Let f(x, t) is integrand which is a function of two variables x and t then
- Take care, here and are replaced in place of t in 2nd & 3rd term.
- If integrand is a function of ‘t’ alone then
Gamma Functions:
Beta function:
Comments
write a comment