Integrate dx
Understand the Problem
The question is asking for the integration of the variable 'x' with respect to 'x', which involves finding the antiderivative of the function 1 with respect to x.
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
- Identify the function to integrate
We want to integrate the function $1$ with respect to $x$. This can be expressed as:
$$ \int 1 , dx $$
- Find the antiderivative
The antiderivative of a constant, like $1$, is simply that constant multiplied by the variable of integration, plus a constant of integration $C$. Therefore, we can write:
$$ \int 1 , dx = x + C $$
- Express the final result
Now we can state the result of our integration clearly, including the constant of integration:
$$ \int 1 , dx = x + C $$
The integral of 1 with respect to x is ( x + C ).
More Information
The constant ( C ) represents any constant value that can be added to the function without changing its derivative. This is essential in integration as it accounts for all possible antiderivatives.
Tips
- Forgetting to include the constant of integration ( C ) can lead to an incomplete answer. Always remember to add it after performing an indefinite integral.
