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## #2268 assume and integration

open
nobody
5
2012-11-18
2011-09-02
bansan
No

Dear,

I try to use assume with integration but it looks like there is a little problem :

(%i1) assume(x>0, a>x, xx>0, l>a, l>0);
(%o1) [x > 0, a > x, xx > 0, l > a, redundant]
(%i2) J(x) := a(x)*b(x)^3/16.*(16./3.-3.364*b(x)/a(x)*(1.-b(x)^3/(12.*a(x)^3)));
3 3
a(x) b (x) 16 3.364 b(x) b (x)
(%o2) J(x) := ---------- (-- - ---------- (1 - --------))
16 3 a(x) 3
12 a (x)
(%i3) a(x) := 1+x/l;
x
(%o3) a(x) := 1 + -
l
(%i4) b(x) := 1+x/l;
x
(%o4) b(x) := 1 + -
l
(%i5) MBx() := (integrate(1/J(x), x, 0, a)/G+kAx)/(integrate(1/J(x), x, 0, l)/G+kAx+kBx)*Mx;
1
integrate(----, x, 0, a)
J(x)
------------------------ + kAx
G
(%o5) MBx() := ------------------------------------ Mx
1
integrate(----, x, 0, l)
J(x)
------------------------ + kAx + kBx
G
(%i6) MBx();
Is l positive, negative, or zero?

But with a different assume :

(%i1) assume(x>0, a>0, xx>0, l>0);
(%o1) [x > 0, a > 0, xx > 0, l > 0]
(%i2) J(x) := a(x)*b(x)^3/16.*(16./3.-3.364*b(x)/a(x)*(1.-b(x)^3/(12.*a(x)^3)));
3 3
a(x) b (x) 16 3.364 b(x) b (x)
(%o2) J(x) := ---------- (-- - ---------- (1 - --------))
16 3 a(x) 3
12 a (x)
(%i3) a(x) := 1+x/l;
x
(%o3) a(x) := 1 + -
l
(%i4) b(x) := 1+x/l;
x
(%o4) b(x) := 1 + -
l
(%i5) MBx() := (integrate(1/J(x), x, 0, a)/G+kAx)/(integrate(1/J(x), x, 0, l)/G+kAx+kBx)*Mx;
1
integrate(----, x, 0, a)
J(x)
------------------------ + kAx
G
(%o5) MBx() := ------------------------------------ Mx
1
integrate(----, x, 0, l)
J(x)
------------------------ + kAx + kBx
G
(%i6) MBx();
4
l l
7.112164765150393 (- - -----------------------------)
3 3 2 2 3
3 l + 9 a l + 9 a l + 3 a
Mx (kAx + -----------------------------------------------------)
G
(%o6) ----------------------------------------------------------------
2.074381389835531 l
kBx + kAx + -------------------
G

Am I doing some thing wrong ?!?
Regards,

## Discussion

• bansan
2011-09-02

Oups...
Maxima version: 5.25.1
Maxima build date: 9:40 9/2/2011
Host type: x86_64-pc-linux-gnu
Lisp implementation type: SBCL
Lisp implementation version: 1.0.36.gentoo-r1

• Barton Willis
2011-09-02

You did nothing wrong--this is a bug.