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Using solve() to find an unknown which is a limit of integration?

asked 2013-05-23 22:28:24 -0500

boyfarrell gravatar image

Is it possible to use the solve() function to find an unknown which is a limit of integration? A trivial example would be,

$$ \int_0^{x^\prime} mx+c \quad dx = 10 $$

where $x^{\prime}$ is the unknown ($m$ and $c$ are both known).

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answered 2013-05-23 23:11:45 -0500

tmonteil gravatar image

updated 2013-05-23 23:14:55 -0500

For such an easy example, Sage is able to do it in the following way:

sage: var('x,c,m,t')
(x, c, m, t)
sage: f(x) = m*x + c

sage: solve([f.integral(x,0,t) == 0], t)
[t == -2*c/m, t == 0]

sage: solve([f.integral(x,0,t) == 10], t)
[t == -(c + sqrt(c^2 + 20*m))/m, t == -(c - sqrt(c^2 + 20*m))/m]
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Asked: 2013-05-23 22:28:24 -0500

Seen: 301 times

Last updated: May 23 '13