Applying Gauss Quadrature to the Falling Parachutist Problem In Example 21.3, we used the multiple-application trapezoidal rule to evaluate d = gm/c ∫0^10[1 - e^-(c/m)t]dt where g = 9.8, c = 12.5, and m = 68.1. The exact value of the integral was determined by calculus to be 289.4351. Recall that

Question

Applying Gauss Quadrature to the Falling Parachutist Problem

In Example 21.3, we used the multiple-application trapezoidal rule to evaluate

[latex]d=\frac{g m}{c} \int_{0}^{10}\left[1-e^{-(c / m) t} ight] d t[/latex]

where g = 9.8, c = 12.5, and m = 68.1. The exact value of the integral was determined by calculus to be 289.4351. Recall that the best estimate obtained using a 500-segment trapezoidal rule was 289.4348 with an [latex]\left|\varepsilon_{t} ight| \cong 1.15 imes 10^{-4}[/latex] percent. Repeat this computation using Gauss quadrature.

Accepted Answer

After modifying the function, the following results are obtained:

Two-point estimate = 290.0145

Three-point estimate = 289.4393

Four-point estimate = 289.4352

Five-point estimate = 289.4351

Six-point estimate = 289.4351

Thus, the fi ve- and six-point estimates yield results that are exact to seven signifi cant fi gures.

Question 22.5: Applying Gauss Quadrature to the Falling Parachutist Problem...

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