Math Problem Statement
Given integral |ln(x)|^2 dx, use 8 sub intervals to find the Tn approximation. Round to 6 decimal places
Solution
To approximate the integral of 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:
Where:
- (the number of subintervals),
- is the width of each subinterval,
- .
Let me know the specific interval for the integral so I can proceed with the calculation!
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Math Problem Analysis
Mathematical Concepts
Numerical Integration
Trapezoidal Rule
Integral of Natural Logarithm
Formulas
Trapezoidal Rule formula: T_n = (Δx/2) [f(x_0) + 2f(x_1) + 2f(x_2) + ... + 2f(x_(n-1)) + f(x_n)]
Δx = (b - a) / n
f(x) = (ln(x))^2
Theorems
-
Suitable Grade Level
Undergraduate
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