Re: automatic integral output simplification

• To: mathgroup at smc.vnet.net
• Subject: [mg115191] Re: automatic integral output simplification
• From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
• Date: Tue, 4 Jan 2011 04:23:08 -0500 (EST)
• References: <ifs310\$opc\$1@smc.vnet.net>

```In[121]:= Integrate[-8 Sin[2 t], {t, 0, t}] // TrigReduce

Out[121]= 4 (-1 + Cos[2 t])

Cheers -- Sjoerd

On Jan 3, 9:57 am, sean k <seaninso... at gmail.com> wrote:
> Hello group,
>
> I want to get around the way Mathematica simplifies the output of an
> integral.
>
> For instance, Let's say you want to integrate -8 sin(2t) from t = {0,
> t}
>
> int1 = \[Integral]-8 Sin[2 t] \[DifferentialD]t
> ul1 = int1;
> ll1 = int1 /. t -> 0;
> ul1 - ll1
>
> yields the correct output.
>
> -4 + 4 Cos[2 t]
>
> But if i pose that integral with limits included in it, Mathematica
> outputs
>
> Integrate[-8 Sin[2 t], {t, 0, t}]
>
> -8 Sin[t]^2
>
> Now both these are correct, except when the definite integral is
> evaluated, "mathematicamagic" kicks in.
>
> My guess is that the coefficient in the argument for the sin function
> is the culprit. What should I do here to make the Mathematica retain
> the "2 t" inside the Sin?
>
> Thanks in advance for any insights.
>
> Sean

```

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