Evaluate the definite integral I = integral 1/x dx [1,3] using the trapezoidal rule method with accuracy ε < 0.05.  (b) Find the error of the results given the exact value of the integral is ln(3).  (c) Improve the results in part (a) using the Romberg method for the same number of subintervals. Find the error of the results by the Romberg method.

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.