Integrate function defined by numerical integration
- To: mathgroup at smc.vnet.net
- Subject: [mg123737] Integrate function defined by numerical integration
- From: Hani <hanisantosa at gmail.com>
- Date: Sat, 17 Dec 2011 02:41:41 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
Hello all, I have a problem. Suppose I have a function:
func[x_] := NIntegrate[ x*Sec[alpha]^2*Exp[-x/Cos[alpha]], {alpha, -
ArcCos[x/2], ArcCos[x/2]}].
Basically the argument of the function, x, also appears as boundary of
integration
Now, when I want to do this integral:
NIntegrate[func[x], {x, 0.2, 1}]
there are error messages: NIntegrate::nlim: alpha = cos^-1(0.5 x) is
not a valid limit of integration. >>
Although in the end, the result appears. Now, how to handle this
problem? I think in this case, we can get the result because func[x_]
itself is simple. But actually my func[x_] is much more complicated,
it contains interpolating function too, and when I do the integral, it
takes long time without result. Can anyone help me?
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