What is the antiderivative of pi?
Understand the Problem
The question is asking for the antiderivative of the constant π (pi). The antiderivative of a constant is the constant multiplied by the variable of integration, plus a constant of integration.
Answer
$$ \int \pi \, dx = \pi x + C $$
Answer for screen readers
$$ \int \pi , dx = \pi x + C $$
Steps to Solve
- Identify the constant for integration
The problem requires the antiderivative of the constant $\pi$.
- Apply the formula for the antiderivative of a constant
The antiderivative of a constant $c$ is given by the formula:
$$ \int c , dx = cx + C $$
where $C$ is the constant of integration.
- Substitute the constant
Using the constant $\pi$, we substitute it into the formula:
$$ \int \pi , dx = \pi x + C $$
- Write the final result
Now we have the final expression for the antiderivative:
$$ \int \pi , dx = \pi x + C $$
$$ \int \pi , dx = \pi x + C $$
More Information
The antiderivative of a constant like $\pi$ follows a straightforward pattern. It illustrates the fundamental concept that the integral of a constant is the constant multiplied by the variable of integration, plus a term representing the general constant of integration, which accounts for all possible vertical shifts of the function.
Tips
- A common mistake is forgetting to include the constant of integration $C$. Always remember that every indefinite integral includes this constant since antiderivatives can differ by a constant.
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