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
- 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 $F'(x) = cos(x)$.
- 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.
- 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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