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The definite integral of \(\sin(t)\) from 3 to 2 is given by:

\[
\int_3^2 \sin(t) \, dt = \cos(3) - \cos(2)
\]

This is the simplified result, and it is in terms of trigonometric cosine values. If you need the numerical approximation:

\[
\cos(3) - \cos(2) \approx -0.1411
\]

Let me know if you'd like more details or further clarification.

Here are five related questions to explore:
1. What is the geometric interpretation of the integral of a sine function?
2. How would the integral change if the limits were swapped (i.e., from 2 to 3)?
3. What is the result of integrating \(\cos(t)\) over the same interval?
4. How can you use substitution to evaluate more complex trigonometric integrals?
5. How does the periodicity of sine and cosine functions affect definite integrals?

**Tip:** Remember, reversing the limits of integration introduces a negative sign!

Evaluate the integral from 3 to 2 of sin(t) dt.

Learn how to solve the definite integral of sin(t) from 3 to 2. This solution involves key concepts from calculus, such as the integral of sin(t), using the Fundamental Theorem of Calculus to compute the result. Suitable for students in Grades 11-12.

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