Given integral |ln(x)|^2 dx, use 8 sub intervals to find the Tn approximation. Round to 6 decimal places

To approximate the integral of \( \left( \ln(x) \right)^2 \) over a given interval using the Trapezoidal Rule with 8 subintervals, we need to know the interval over which the integral is to be calculated. The Trapezoidal Rule formula is:

\[
T_n = \frac{\Delta x}{2} \left[ f(x_0) + 2f(x_1) + 2f(x_2) + \cdots + 2f(x_{n-1}) + f(x_n) \right]
\]

Where:
- \( n = 8 \) (the number of subintervals),
- \( \Delta x = \frac{b - a}{n} \) is the width of each subinterval,
- \( f(x) = \left( \ln(x) \right)^2 \).

Let me know the specific interval \([a, b]\) for the integral so I can proceed with the calculation!

Given integral |ln(x)|^2 dx, use 8 sub intervals to find the Tn approximation. Round to 6 decimal places.

Learn how to approximate the integral of (ln(x))^2 using the Trapezoidal Rule with 8 subintervals. This problem covers key numerical integration concepts, including the formula for Tn approximation and step-by-step calculations. Suitable for undergraduate students.

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