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Constructions in Sage: A Sage cookbook |  |
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Constructions in Sage: A Sage cookbook | |
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Numerical integration is discussed in §2.2.2 below.
Sage can integrate some simple functions on its own:
sage: f = x^3 sage: f.integral() x^4/4 sage: integral(x^3,x) x^4/4 sage: f = x*sin(x^2) sage: integral(f,x) -cos(x^2)/2
Sage can also compute symbolic definite integrals involving limits.
sage: var('x, k, w')
(x, k, w)
sage: f = x^3 * e^(k*x) * sin(w*x)
sage: print f.integrate(x)
6 3 4 5 2 7 3
(((k w + 3 k w + 3 k w + k ) x
6 2 4 4 2 6 2 4 3 2 5
+ (3 w + 3 k w - 3 k w - 3 k ) x + (- 18 k w - 12 k w + 6 k ) x
4 2 2 4 k x
- 6 w + 36 k w - 6 k ) e sin(w x)
7 2 5 4 3 6 3 5 3 3 5 2
+ ((- w - 3 k w - 3 k w - k w) x + (6 k w + 12 k w + 6 k w) x
5 2 3 4 3 3 k x
+ (6 w - 12 k w - 18 k w) x - 24 k w + 24 k w) e cos(w x))
8 2 6 4 4 6 2 8
/(w + 4 k w + 6 k w + 4 k w + k )
sage: integrate(1/x^2, x, 1, infinity)
1
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Constructions in Sage: A Sage cookbook | |
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