The trapezoidal approximation of the integral $\int_1^3 e^x \, dx$ using 10 trapezoids gives an approximate value of $17.43$. The graph above shows the trapezoidal approximation (orange areas) under the curve of $f(x) = e^x$ from $x = 1$ to $x = 3$, with the trapezoids summing to the approximation.

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Here are five related questions to consider:

1. How does the accuracy of the trapezoidal rule change with increasing $n$?
2. What is the exact value of $\int_1^3 e^x \, dx$, and how close is it to the approximation?
3. Can we use Simpson's Rule to get a more accurate result for this integral?
4. How would the graph look if $n = 5$ or $n = 20$ trapezoids were used?
5. What are other numerical integration techniques, and how do they compare to the trapezoidal rule?

Tip: The accuracy of the trapezoidal rule improves as the number of subintervals increases, but for functions that curve significantly, other methods like Simpson's rule might offer better accuracy.