Sine Integral The theory of diffraction produces the sine
Chapter 5, Problem 50E(choose chapter or problem)
Sine Integral The theory of diffraction produces the sine integral function
\(\mathrm{Si}(x)=\int_{0}^{x} \frac{\sin t}{t} d t\). Use the Midpoint Rule to approximate Si (1) and Si (10). (Recall that \(\lim _{x \rightarrow 0}(\sin x) / x=1\).) Experiment with the number of subintervals until you obtain approximations that have an error less than \(10^{-3}\). A rule of thumb is that if two successive approximations differ by less than \(10^{-3}\), then the error is usually less than \(10^{-3}\).
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