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

$4x + C$

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.

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