## How to integrate a piecewise function?

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 How to integrate a piecewise function? Peng Yu 10/9/12 1:49 PM Hi, The function g down below is not integrated correctly. I can not find the corresponding page in the manual for solving this problem. Does anybody know how to define a piecewise function and integrate it? Thanks! ~/linux/test/sage/man/sage/symbolic/integration/integral/definite_integral\$ cat ./main1.sage #!/usr/bin/env sage from sage.symbolic.integration.integral import definite_integral def f(x):   return (1-x^2)^3 def g(x):   if x>=0:     return (1-x^2)^3   else:     return 0 print definite_integral(f(x),x,-1,1) print definite_integral(g(x),x,-1,1) ~/linux/test/sage/man/sage/symbolic/integration/integral/definite_integral\$ ./main1.sage 32/35 0 -- Regards, Peng Re: [sage-support] How to integrate a piecewise function? David Joyner 10/9/12 1:57 PM On Tue, Oct 9, 2012 at 4:49 PM, Peng Yu wrote: > Hi, > > The function g down below is not integrated correctly. I can not find > the corresponding page in the manual for solving this problem. Does > anybody know how to define a piecewise function and integrate it? From the documentation: sage: f1(x) = -1 sage: f2(x) = 2 sage: f = Piecewise([[(0,pi/2),f1],[(pi/2,pi),f2]]) sage: f.integral() Piecewise defined function with 2 parts, [[(0, 1/2*pi), x |--> -x], [(1/2*pi, pi), x |--> -3/2*pi + 2*x]] sage: f.integral(definite=True) 1/2*pi > Thanks! > > ~/linux/test/sage/man/sage/symbolic/integration/integral/definite_integral\$ > cat ./main1.sage > #!/usr/bin/env sage > > from sage.symbolic.integration.integral import definite_integral > > def f(x): >   return (1-x^2)^3 > > def g(x): >   if x>=0: >     return (1-x^2)^3 >   else: >     return 0 > > print definite_integral(f(x),x,-1,1) > print definite_integral(g(x),x,-1,1) > > ~/linux/test/sage/man/sage/symbolic/integration/integral/definite_integral\$ > ./main1.sage > 32/35 > 0 > > -- > Regards, > Peng > > -- > You received this message because you are subscribed to the Google Groups "sage-support" group. > To post to this group, send email to sage-s...@googlegroups.com. > To unsubscribe from this group, send email to sage-support...@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-support?hl=en. > >