The table gives values of f(x)=e−x2 rounded to four decimal places. xf(x)01.00000.250.93940.500.77880.750.56981.000.3679 Use Simpson’s rule with four equal intervals to approximate ∫01e−x2dx.
The interval width is h=(1−0)/4=0.25. Simpson’s rule gives I≈3h[f0+4f1+2f2+4f3+f4]. Substituting the table values, I≈30.25[1+4(0.9394)+2(0.7788)+4(0.5698)+0.3679]=0.746858…≈0.7469.
Uses the correct Simpson weights.
[2 marks]
Substitutes the table values and interval width.
[1 mark]
Calculates the approximation.
[1 mark]
Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.