Question

Properties Of Indefinite Integral

Answer 1

Answer:

An integral which is not having any upper and lower limit is known as an indefinite integral.

Mathematically, if F(x) is any anti-derivative of f(x) then the most general antiderivative of f(x) is called an indefinite integral and denoted,

∫f(x) dx = F(x) + C

Explanation:Indefinite Properties

Let us now look into some properties of indefinite integrals.

Property 1: The process of differentiation and integration are inverses of each other in the sense of the following result.

Property 2: Two indefinite integrals with the same derivative lead to the same family of curves, and so they are equivalent.

Property 3: The integral of the sum of two functions is equal to the sum of integrals of the given functions.

Property 4:

For a finite number of functions f1, f2…. fn and the real numbers p1, p2…pn,

∫[p1f1(x) + p2f2(x)….+pnfn(x) ]dx = p1∫f1(x)dx + p2∫f2(x)dx + ….. + pn∫fn(x)dx