Arc length

2/20/13 Arc length -- Sage
Arc length
@interact
def _(Function = sin(x), a = 0,b = pi, n=4):
f(x)=Function
dx = ((b-a)/n)
k=var('k')
m(k) = (f(a+k*dx) - f(a + (k-1)*dx))/dx
S= dx*sum([sqrt(1+(m(k))^2) for k in [1..n]])
html('Arc length approximation: $%s$' %N(S))
g=diff(f,x)
html('Exact arc length: $%s$'
%numerical_integral(sqrt(1+g(x)^2),a,b)[0])
#show(N(integral(sqrt(1+g(x)^2),(x,a,b))))
p = plot( f(x), (x, a, b), color='green')
#the old way that was less efficient
#show(p+ sum(plot(f(a+k*dx)+m(k)*(x-(a+k*dx)), (x, a+(k-
1)*dx, a+k*dx ), figsize=4 ) for k in [1..n]))
q = line([(a+k*dx, f(a+k*dx)) for k in [0..n]])
show(p+q, figsize = 4)
Function sin(x)
a 0
b pi
n 4
Arc length approximation:
Exact arc length:
3.79009130853072
3.82019778903
test.sagenb.org/home/Carlos_Rodriguez/21/print 1/2

2/20/13 Arc length -- Sage
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