https://file.aiquickdraw.com/mathbot/file/172613697983318me3nbk.jpg

The statement in the image is **True**.

In integral calculus, the property of definite integrals states that:

\[
\int_b^a f(x)\,dx = -\int_a^b f(x)\,dx.
\]

This means that swapping the limits of integration introduces a negative sign. If you integrate from \( b \) to \( a \), it's equivalent to integrating from \( a \) to \( b \) with a minus sign. Therefore, the definition given is correct.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. What is the geometric interpretation of a definite integral?
2. How does the fundamental theorem of calculus relate to definite integrals?
3. What does it mean for a function to be integrable on an interval?
4. How do you handle the integral of a piecewise function over different intervals?
5. Can you explain how definite integrals apply to calculating areas under curves?

**Tip:** Always pay attention to the limits of integration, as reversing them changes the sign of the result.

If f is integrable on the [a, b], then we define ∫_b^a f(x) dx = - ∫_a^b f(x) dx. True or False?

Explore the key property of definite integrals that involves reversing the limits of integration. The problem tests the understanding of integral calculus concepts, specifically that ∫_b^a f(x) dx = -∫_a^b f(x) dx.

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