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Re: automatic integral output simplification

  • To: mathgroup at smc.vnet.net
  • Subject: [mg115212] Re: automatic integral output simplification
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Tue, 4 Jan 2011 04:27:03 -0500 (EST)

Integrate[-8 Sin[2 t], {t, 0, t}]

-8 Sin[t]^2

% // TrigReduce

4 (-1 + Cos[2 t])


Bob Hanlon

---- sean k <seaninsocal 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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