What is the antiderivative of 4?
Understand the Problem
The question is asking for the antiderivative (or indefinite integral) of the constant 4. The antiderivative of a constant 'a' is 'ax + C', where 'C' is the constant of integration.
Answer
$4x + C$
Answer for screen readers
The antiderivative of 4 is $4x + C$.
Steps to Solve
- Identify the constant to integrate
We are asked to find the antiderivative of the constant 4. We recognize that this will involve applying the formula for the antiderivative of a constant.
- Apply the antiderivative formula
According to the formula for finding the antiderivative of a constant $a$, we have:
$$ \int a , dx = ax + C $$
In our case, $a$ is 4.
- Substitute the constant into the formula
Now we substitute 4 into the formula:
$$ \int 4 , dx = 4x + C $$
This gives us the result for the antiderivative of the constant 4.
The antiderivative of 4 is $4x + C$.
More Information
The constant $C$ represents any constant value that can be added to the function, since the derivative of a constant is zero. This is important in calculus as it indicates that there are infinitely many antiderivatives for a given function, differing by a constant.
Tips
- Forgetting to add the constant of integration $C$. Always remember that indefinite integrals include this constant.