Re: Piecewise Integration Woes

*To*: mathgroup at smc.vnet.net*Subject*: [mg63399] Re: [mg63388] Piecewise Integration Woes*From*: pdesai1 at umbc.edu*Date*: Thu, 29 Dec 2005 02:57:30 -0500 (EST)*References*: <200512280855.DAA28668@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

> mathgroup at smc.vnet.net; Tue, 27 Dec 2005 17:33:45 -0600 (CST) > From: Bruce Colletti <vze269bv at verizon.net> To: mathgroup at smc.vnet.net > Subject: [mg63399] [mg63388] Piecewise Integration Woes > > Re Mathematica 5.2 under WinXP. > > h, g, and (presumably f) are continuous functions. > > So, what causes the NIntegrate::slwcon warning? Although continuous, > g(h(x)) isn't always differentiable. Could this be the cause? > > Thankx. > > Bruce > > ------------ > > > T = {{16, 113.32}, {20, 68.11}, {900, 0.15}, {1000, 0.13}}; > > f = Interpolation@T; > > h[r_] := Piecewise[{{T[[1, 2]], r < T[[ > 1, 1]]}, {f@r, T[[1, 1]] <= r < T[[-1, 1]]}}, T[[-1, 2]]]; > > g[x_] := Piecewise at {{0.99, 29 <= x}, {0.99(x - 14.5)/(29 - > 14.5), 14.5 <= x < 29}} > > NIntegrate[g[h@r], {r, 14, 40}, MaxRecursion -> 30] > > Have you tried PiecewiseExpand NIntegrate[g[h@r]//PiecewiseExpand, {r, 14, 40}, MaxRecursion -> 30] it seems to work without spitting any error Version 5.1.1 for windows Hope this helps Pratik