Double Math

# Integral of a Constant

In order to compute the answer of the integration, the Constant of Integration must be added. Through this anti-derivative process, it was not possible to obtain the constant term from the original function. It is written as +C and can have any value.

A constant K is integrated with respect to x as follows:

Kx + C

What is the integral of a constant?

When x is an independent variable, the derivative of Kx is equal to K. This equation can be written as y = Kx – 0, a line with a constant slope of K.

By the fundamental theorem of calculus

The indefinite integral of any constant function C with respect to x.

\;\;\;\;\;\;\;\int Cdx\ .

=Cx+D\ .

The Derivative of a Constant

if

f(x)=c\ .

f'(x)=\frac d{dx}(c)\ .

f'(x)=0\ .

## Why Is the Derivative of a Constant Zero?

A derivative function is dy/dx, which means that y changes with x, and vice versa. Therefore, the value of y depends on the value of x. When the last change approaches zero, a derivative is a function’s change ratio corresponding to its independent variable’s change.

No matter what variable is changed in a function, a constant remains constant. In a particular equation, a constant always exists, regardless of all the other variables.

Example:

Find the derivative of 11.

f(x)=11 .

f'(x)=\frac d{dx}(11) .

f'(x)=0 .