3706.sagews

Left Hand Riemann Sums

Type in your own f(t), a, b, and n. Then click evaluate.

var ('t')
f(t)=cos(t)
a=-5
b=5
n=10

Click evaluate.

def left_riemann_plot(f, a, b, n):
    p = plot(f, a, b, thickness=2)
    deltax = (b-a)/n
    rectops = Piecewise([[(a+j*deltax, a+(j+1)*deltax),f(a+(j+1)*deltax)] for j in range(n)])
    prectops = plot(rectops, color='magenta', fill='axis', fillcolor='magenta')
    outline = []
    for j in range(n):
        outline = outline + [(a+j*deltax,0), (a+j*deltax,f(a+(j+1)*deltax)), (a+(j+1)*deltax,f(a+(j+1)*deltax)), (a+(j+1)*deltax, 0)]
    poutline = plot(line(outline, rgbcolor='black'))
    show(p + prectops + poutline)

Click Evaluate.

def left_riemann_value(f, a, b, n):
    deltax = (b-a)/n
    return(sum(f(a+(j+1)*deltax)*deltax for j in range(n)))

Click Evaluate and you will see the Graph.

left_riemann_plot(f,a,b,n)

Click evaluate to see the solution.

left_riemann_value(f,a,b,n).n()

-1.75529911082289

Hope you had enjoyed this! I did not use the "my list" you had provided, however, this code works for all functions.

Thank You.