Consider Table 2. Table 2: Data for curve fitting I f(x) 1.6 4.953 1.8 6.050 2.0...

 

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Consider Table 2. Table 2: Data for curve fitting I f(x) 1.6 4.953 1.8 6.050 2.0 7.389 2.2 9.025 2.4 11.023 2.6 13.464 2.8 16.445 3.0 20.086 3.2 24.533 3.4 29.964 3.6 36.598 3.8 44.701 (1.1) Use the trapezoidal rule to estimate the integral from = 1.8 to x = 3.4, using a hand calculator. (1.2) Solve (1.1) using a mathematica program. (5) (5) (1.3) Replace the trapezoidal rule in (1.1) with the Romberg integration rule, then integrate with a calculator and a mathematica program. (10) Consider Table 2. Table 2: Data for curve fitting I f(x) 1.6 4.953 1.8 6.050 2.0 7.389 2.2 9.025 2.4 11.023 2.6 13.464 2.8 16.445 3.0 20.086 3.2 24.533 3.4 29.964 3.6 36.598 3.8 44.701 (1.1) Use the trapezoidal rule to estimate the integral from = 1.8 to x = 3.4, using a hand calculator. (1.2) Solve (1.1) using a mathematica program. (5) (5) (1.3) Replace the trapezoidal rule in (1.1) with the Romberg integration rule, then integrate with a calculator and a mathematica program. (10)