To approximate ∫01e−x2dx to three decimal places, which of the following approaches is most appropriate?
a) Apply the substitution u=−x2 to obtain an elementary antiderivative and evaluate directly.
b) Use a single trapezoidal estimate on [0,1]; the smoothness of e−x2 guarantees three-decimal accuracy.
c) Expand e−x2 into its Maclaurin series and sum enough terms until the remainder is less than 10−3.
d) Rewrite e−x2 as (e−x)x and integrate by treating the exponent as a parameter.