Given a piecewise function f[t_]:=Piecewise[{{Exp[-1/t^2],t>0},{0,x<=0}}], I can define another function like this: g[t_]:=f[t+1]f[1-t]. Both the functions can be calculated and plotted. But when I define the third function h[t_]:=Integrate[g[x],{x,-:inf:,t}], h[t] cannot be used to plot. Does the definition for h[t] have anything wrong?
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1 Answer
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You have an error in the definition of f[] and it's faster to use NIntegrate[]:
f[t_] := Piecewise[{{Exp[-1/t^2], t > 0}, {0, t <= 0}}]
g[t_] := f[t + 1] f[1 - t]
h[t_] := NIntegrate[g[x], {x, -Infinity, t}]
Plot[h[t], {t, -1, 1}]
answered Jan 29, 2015 at 5:11
x <= 0ort <= 0inf? $\endgroup$gbe modified tog[t_] = f[t + 1] f[1 - t] // PiecewiseExpand // Simplify$\endgroup$