To solve the given problem using the Trapezoidal Rule with $n = 4$, let's break it into steps:

Step 1: Interval and Subintervals

The interval is $[0, 8]$, and $n = 4$. The width of each subinterval ($h$) is:

$h = \frac{b-a}{n} = \frac{8-0}{4} = 2$

Subinterval points are: $x_0 = 0, \, x_1 = 2, \, x_2 = 4, \, x_3 = 6, \, x_4 = 8$

Step 2: Trapezoidal Rule Formula

The Trapezoidal Rule formula is:

$\int_a^b f(x) \, dx \approx \frac{h}{2} \left[ f(x_0) + 2f(x_1) + 2f(x_2) + 2f(x_3) + f(x_4) \right]$

Here, we need $f(x)$ evaluated at these points. However, the problem might expect an expression or provided function values at specific points.

Step 3: Approximating the Integral

To approximate the integral, plug in the values of $f(x_0), f(x_1), f(x_2), f(x_3),$ and $f(x_4)$ as provided or as symbolic representations.

If specific function values $f(x)$ were not listed in the problem, it would indicate the task is for conceptual understanding rather than computation.

Would you like me to continue with a hypothetical example or assist further if additional information is provided?

Here are related queries for deepening your understanding:

1. How does the Trapezoidal Rule compare to Simpson’s Rule?
2. Can the Trapezoidal Rule be derived geometrically?
3. How does increasing $n$ improve accuracy in the Trapezoidal Rule?
4. What are the error bounds for the Trapezoidal Rule?
5. How can $f(x)$ values influence numerical integration?

Tip: Always ensure subintervals are of equal width in numerical methods for accuracy.