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.
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The Derivative of a Constant
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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.
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