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The value of the definite integral of \( 2t^3 + 3t^2 - t + 1 \) from \( a = 8 \) to \( b = 14 \) is approximately \( 19332 \) when rounded to the nearest unit.

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Here are five related questions for practice:
1. What is the indefinite integral of \( 2t^3 + 3t^2 - t + 1 \)?
2. How would the result change if the limits of integration were \( a = 0 \) and \( b = 14 \)?
3. How do you apply the Fundamental Theorem of Calculus to solve this integral?
4. What happens to the integral value if the coefficient of \( t^3 \) is changed to 1?
5. What is the geometric interpretation of a definite integral in this context?

**Tip:** When integrating polynomials, remember that each term's power increases by one, and the new term is divided by the new power.

Integrate (2t^3 + 3t^2 - t + 1) dt, where a=8 and b=14. State your answer to the nearest unit.

Learn how to compute the definite integral of 2t^3 + 3t^2 - t + 1 with limits from a = 8 to b = 14. The final value is approximately 19332, rounding to the nearest unit. This solution uses key concepts from integral calculus and the Fundamental Theorem of Calculus.

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