The exact value of the area under the curve defined by the given parametric equations over the interval \(5 \leq t \leq 9\) is \(-\frac{111288}{5}\).

This simplifies to approximately \(-22,257.6\). The negative sign indicates that the area lies below the x-axis for the given interval.

Would you like to explore more about the meaning of the negative area or any other aspect of this calculation?

### Related Questions
1. How can we interpret a negative area in the context of parametric curves?
2. What would be the effect on the area calculation if the interval were reversed?
3. How can we find the total length of the curve defined by parametric equations?
4. Can this method be applied to non-polynomial parametric equations?
5. How does this area relate to the area under a regular Cartesian curve?

**Tip:** Always ensure the context of the problem aligns with the interpretation of negative or positive area results.

Discover how to calculate the exact area under the curve defined by parametric equations over the interval [5, 9]. The area is approximately -22,257.6, indicating it lies below the x-axis. Explore interpretations of negative area in parametric curves.

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