Question

Why do we use a constant in Integration?

Answer 1

Constant in Integration

The constant of integration is used to represent the term of the original expression, which cannot be obtained from the antiderivative of the function

• A constant of integration is used in indefinite integrals.
• An integral of a function is the antiderivative of the function.
• A constant of integration is denoted as $C$ and it can be any real number depending on the function.
• While differentiating a function, the derivative of a constant is zero. So while finding the antiderivative, the antiderivative of the constant is not present. So the constant of integration is written for an indefinite integral.

For example, $f\left(x\right)=xandg\left(x\right)=x+4$

By differentiating the function we get $f\text{'}\left(x\right)=1andg\text{'}\left(x\right)=1$

Again while finding the antiderivative, $F\left(x\right)=xandG\left(x\right)=x$. Here $g\left(x\right)$ need to be equal to $G\left(x\right)$ so the function $G\left(x\right)=x+C$, where $C$ is the constant of integration.