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Re : definite and indefinite Integrate
*To*: mathgroup at smc.vnet.net
*Subject*: [mg50441] Re : [mg50428] definite and indefinite Integrate
*From*: "Florian Jaccard" <florian.jaccard at eiaj.ch>
*Date*: Sat, 4 Sep 2004 01:43:17 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
They are not equal, but opposite!
Read the Newton-Leibnitz formula...
But you have to tell Mathematica what you seem to assume, that your y and y0
are positive (so they are real...)
In[51]:=
ff[z_] = 1/z + z^3;
In[52]:=
a = Integrate[ff[z], {z, y, y0}, Assumptions ->
{y > 0, y0 > 0}]
Out[52]=
(1/4)*(-y^4 + y0^4) + Log[y0/y]
In[53]:=
intff[z_] = Integrate[ff[z], z]
Out[53]=
z^4/4 + Log[z]
In[54]:=
b = intff[y] - intff[y0]
Out[54]=
y^4/4 - y0^4/4 + Log[y] - Log[y0]
In[55]:=
Simplify[a == -b, {y > 0, y0 > 0}]
Out[55]=
True
Regards
F.Jaccard
-----Message d'origine-----
De : Jun Yan [mailto:jyan at stat.wisc.edu]
Envoyé : vendredi, 3. septembre 2004 09:35
À : mathgroup at smc.vnet.net
Objet : [mg50428] definite and indefinite Integrate
This is a question from a beginner:
ff[z_] = 1/z + z^3
Integrate[ff[z], {z, y, y0}]
intff[z_] = Integrate[ff[z], z]
intff[y] - intff[y0]
I expected to get same results from line 2 and line 4. However, the output
from line 2 is very complicated, with an If which has Im(y) and Im(y0)
involved. The result I want is that from line 4. How can I modify line 2
so that it produces the same output as from line 4?
Thanks.
Jun
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