What is the integral of 1 dx?
Understand the Problem
The question is asking for the integral of the function 1 with respect to the variable x, which is a basic concept in calculus. The high-level approach to solve it involves applying the rules of integration.
Answer
The integral of 1 with respect to \( x \) is \( x + C \).
Answer for screen readers
The integral of 1 with respect to ( x ) is ( x + C ).
Steps to Solve
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Identify the integral to solve
We want to find the integral of the function 1 with respect to the variable ( x ). This can be written as:
$$ \int 1 , dx $$ -
Apply the basic integration rule
The integral of a constant (in this case, 1) with respect to ( x ) is simply the constant multiplied by ( x ). Thus, we will have:
$$ \int 1 , dx = x + C $$
where ( C ) is the constant of integration. -
Final expression
Representing the result clearly, we can say:
The integral of 1 with respect to ( x ) is:
$$ x + C $$
The integral of 1 with respect to ( x ) is ( x + C ).
More Information
This integral shows a fundamental rule in calculus where integrating a constant results in that constant multiplied by the independent variable, plus a constant of integration. The constant ( C ) represents any constant value since the process of integration can only determine the function up to a constant.
Tips
- Forgetting to include the constant of integration ( C ) at the end of the result. Always remember that indefinite integrals have an arbitrary constant.
