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For the two questions:

1. **Integral \( \int_{4.7}^{7.0} t^9 \, dt \):**
   - The result of this integral is approximately **27,721,533.6**. This matches the option \( \boxed{27,721,533.6} \).

2. **Integral \( \int_{-1.15}^{1.74} e^{2.12x} \, dx \):**
   - The result is approximately **18.83**, matching the option \( \boxed{18.83} \).

Would you like more detailed steps or clarifications on how these integrals were solved? Here are 5 related questions to consider:

1. How is the power rule applied when integrating polynomials?
2. What is the fundamental theorem of calculus, and how does it apply here?
3. How do you integrate exponential functions in general?
4. What methods are useful for approximating integrals numerically?
5. How does the definite integral differ from the indefinite integral?

**Tip:** For integrals involving exponential functions, the coefficient of the variable inside the exponent plays a key role in determining the antiderivative.

Evaluate the following integrals: 1. \( \int_{4.7}^{7.0} t^9 \, dt \) and 2. \( \int_{-1.15}^{1.74} e^{2.12x} \, dx \).

This page explains how to evaluate the definite integrals of a polynomial function \( t^9 \) and an exponential function \( e^{2.12x} \) over given intervals. The solutions apply calculus concepts and the Fundamental Theorem of Calculus.

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