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integral function

• To: mathgroup at smc.vnet.net
• Subject: [mg31679] integral function
• From: "Higinio Ramos" <higra at usal.es>
• Date: Sat, 24 Nov 2001 16:43:50 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

I have a function expressed in integral form, where the integral cannot 
be made,
y[t _ ]: = Integrate[Exp[Cos[s]]*Sin[t - s ], { s, 0, t } ]. 
Nevertheless, if I indicate Mathematica that draws, it does. 
Plot[y[t],{t,0,1}].
What happens, does it make the numerical integration ?. How does it make 
it, with what precision, what method?
On the other hand, the function Derivative does not make it correctly, 
it simply derives the part from the function integrating that depends on 
the variable t although by hand it can be obtained without difficulty, 
(and even with Mathematica, expanding previously the function Sin[t-s]). 
Why?
Thanks

Higinio Ramos