# JEE Main & Advanced Mathematics Definite Integrals Definition

Definition

Category : JEE Main & Advanced

Let $\varphi (x)$ be the primitive or anti-derivative of a function $f(x)$ defined on $[a,\,\,b]$ i.e., $\frac{d}{dx}[\varphi (x)]=f(x)$. Then the definite integral of  $f(x)$ over $[a,\,\,b]$ is denoted by $\int_{a}^{b}{f(x)dx}$ and is defined as $[\varphi (b)-\varphi (a)]$ i.e., $\int_{a}^{b}{f(x)dx=\varphi (b)-\varphi (a)}$. This is also called Newton Leibnitz formula.

The numbers $a$ and $b$ are called the limits of integration, $'a'$ is called the lower limit and $'b'$ the upper limit. The interval $[a,\,\,b]$is called the interval of integration. The interval $[a,\,\,b]$ is also known as range of integration. Every definite integral has a unique value.

You need to login to perform this action.
You will be redirected in 3 sec