https://file.aiquickdraw.com/mathbot/file/17285881322956mv7or0p.jpg

The image shows a problem where we are asked to find the value of the definite integral:

\[
\int_{-a}^{3a} f(x)\, dx
\]

given that \( a = 2 \).

However, the function \( f(x) \) is not specified in the image. If you can provide the function \( f(x) \), I can help you compute the integral and round it to four decimal places, as requested.

Do you want to clarify the function \( f(x) \) or provide any additional details?

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Here are five related questions:

1. What is the function \( f(x) \) in this integral problem?
2. Do you know any methods for solving definite integrals, such as the Fundamental Theorem of Calculus?
3. Could this integral have symmetry properties that simplify it?
4. How does changing the limits of integration affect the result of the integral?
5. Why do we round answers in calculus problems to a specific number of decimal places?

**Tip**: When solving definite integrals, always check if the function is odd or even, as this can sometimes simplify the calculation, especially for symmetric limits.

If a = 2, then find the value of the definite integral from -a to 3a of f(x) dx. Round your final answer to 4 decimal places.

This problem involves calculating the value of a definite integral of f(x) with given limits from -a to 3a. Learn how to apply the Fundamental Theorem of Calculus and round your final answer to four decimal places.

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