Pseudocode for Riemann Sums

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• Misc
  • Exam 1 solution available through our “Exercises” page
• Questions?
• Integration
  • Examples of what it should do
    • One function to calculate and plot Riemann sums
      

      >> f = @(x) x * sin(x);
      >> riemann( f, 0, pi, 10 )
      ans =
          3.1157

      
      
    • Similar function to calculate and plot according to trapezoid rule
      

      >> trapezoid( f, 0, pi, 8 )
      ans =
          3.1011

      
      
    • And finally a script to plot how both methods approximate actual integral as number of intervals grows
      
  • Pseudocode
    

    riemann( f, a, b, n )
        delta = (b-a)/n
        total = 0
        xs = linspace(a,b,1000)
        plot xs, f(xs)
        hold on
            for i = a : delta : b-delta            % sigma
                % left sum
                i1 = i + delta
                x = [ i, i1, i1, i, i ]
                y = [ 0, 0, f(i), f(i), 0 ]
                plot x, y                          % current rectangle
                total = total + delta * f(i)
            end of for
            return total

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  • Lab day for integration lab

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