What is the antiderivative of cos x?

Understand the Problem

The question is asking for the antiderivative, or indefinite integral, of the function cos(x). The antiderivative will give us a function whose derivative is cos(x).

Answer

The antiderivative of $cos(x)$ is $sin(x) + C$.
Answer for screen readers

The antiderivative of $cos(x)$ is $sin(x) + C$.

Steps to Solve

  1. Identify the function to integrate

We need to find the antiderivative of $cos(x)$. This means we are looking for a function $F(x)$ such that $F'(x) = cos(x)$.

  1. Recall the antiderivative of cosine

The antiderivative of $cos(x)$ is a known result. We use the fact that:

$$ \int cos(x) , dx = sin(x) + C $$

where $C$ is the constant of integration.

  1. Write down the final result

Now we can formally state the result of our integration:

$$ F(x) = sin(x) + C $$

This tells us that the indefinite integral of $cos(x)$ is $sin(x)$ plus a constant.

The antiderivative of $cos(x)$ is $sin(x) + C$.

More Information

The constant $C$ represents an arbitrary constant that arises from indefinite integrals, indicating that there are infinitely many functions with the same derivative.

Tips

  • A common mistake is forgetting to include the constant of integration, $C$. Always remember to add it when calculating indefinite integrals.
  • Another mistake might be to confuse the antiderivative with the derivative. Make sure you're integrating if you're looking for antiderivatives.
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