What is the integral of pi?
Understand the Problem
The question is asking for the integral of the mathematical constant π (pi). This typically refers to the indefinite integral where π is treated as a constant and the integral can be computed accordingly.
Answer
$$ \int \pi \, dx = \pi x + C $$
Answer for screen readers
The integral of π with respect to x is given by: $$ \int \pi , dx = \pi x + C $$
Steps to Solve
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Identify the Integral We are looking for the indefinite integral of the constant $\pi$.
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Apply the Integral Rule The integral of a constant $c$ with respect to $x$ is given by the formula: $$ \int c , dx = cx + C $$ where $C$ is the constant of integration.
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Substitute Pi into the Formula Now, substitute $\pi$ for $c$: $$ \int \pi , dx = \pi x + C $$
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State the Result Hence, the result of the integral is: $$ \int \pi , dx = \pi x + C $$
The integral of π with respect to x is given by: $$ \int \pi , dx = \pi x + C $$
More Information
The integral of a constant is an essential concept in calculus. It reflects how the area under the curve of a constant function changes with respect to the variable of integration (in this case, $x$).
Tips
- Forgetting to include the constant of integration $C$, which is crucial in indefinite integrals.
- Misunderstanding that constants do not change based on the variable of integration.
