On Nov 20, 2007 8:12 AM, [EMAIL PROTECTED]
<[EMAIL PROTECTED]> wrote:
>
> As far as i know, length of curve, defined as
> f(x)
> from a to b (a <= x <= b) is
> L = integral from a to b of sqrt(1 + df(x)^2)dx
> where df(x) is diff(f,x)
>
> for f(x) = y = x^2 , a=0, b=2 it should be
> df(x)=2x
> sqrt(17) + ln|4 + sqrt(17)|/4
>
> which is 4.647
>
> however, SAGE thinks differently. For this code:
>
> y = x^2
> dy = diff(y,x)
> z = integral(sqrt(1 + dy^2), x, 0, 2)
> print(z)
> print(RR(z))
>
> output is
>
> 4 sqrt(17) + 4
> --------------
> 4
> 5.12310562561766
>
> Am i doing something wrong?
No. Maxima gives
(%i2) integrate (sqrt(1+4*x^2), x, 0, 2);
asinh(4) + 4 sqrt(17)
(%o2) ---------------------
4
so possibly SAGE is not parsing that properly? That's the only thing I can think
of. The following just confirms your computation:
sage: sqrt(1 + (2*x)^2).nintegrate(x, 0, 2)
(4.6467837624329427, 1.5663635326179329e-09, 21, 0)
sage: integral(sqrt(1 + (2*x)^2), x, 0, 2)
(4 + 4*sqrt(17))/4
sage: RR(integral(sqrt(1 + (2*x)^2), x, 0, 2))
5.12310562561766
> >
>
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