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
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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)
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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)))
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Click Evaluate and you will see the Graph.
left_riemann_plot(f,a,b,n)
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Click evaluate to see the solution.
left_riemann_value(f,a,b,n).n()
-1.75529911082289 -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.
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