Consider the integral Integral x^-2/3 exp (-x^2)dx between the limits 0 and 1 Th

Question

Consider the integral Integral x^-2/3 exp (-x^2)dx between the limits 0 and 1 The integrand is singular, although it is integrable (Can you prove this?). (a) Apply Composite Midpoint method with suitable number of panels, approximate the above integral. (b) Make the change of variables x = u^a in this integral. What values of cr give a transformed integral that is appropriate for Composite Simpson Rule? Using the smallest value of alpha, approximate the integral by Simpson Composite Rule with suitable number of panels. Are the results obtained from (a) and (b) same? Explain your findings.

Explanation / Answer

Consider the integral Integral x^-2/3 exp (-x^2)dx between the limits 0 and 1 Th

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