Advanced Search

Question: Maple integration vs manual integration and testing relations

Question:Maple integration vs manual integration and testing relations

hexsol 30 Maple 2023
integration assumptions combine
December 13 2024
0

Hi!

So I like to check that my manual integrations and/or maple integrations are equal with each other. I normally do this using the Test Relation function.

I was working on a problem and noticed that Maple didn't evaluate the integrals being the same, even though they presumedly are.

Could anyone shed some light on why I get this inequality?

Thanks in advance!

mapleintvsmanualint.mw

restartNULL

dn/dt = -r__S*V

 

We can define n as C*V 

dC*V/dt = -r__S*V

 

We can define the concentration C as S  

dS/dt = -r__S

 

where -r__S = V__max*[S]/(1+K__1*[S]+K__2*[S^2])

  

ds/dt = -V__max*[S]/(1+K__1*[S]+K__2*[S^2])=

 

1/dt = -V__max*[S]/((1+K__1*[S]+K__2*[S^2])*ds)

 

dt = (1+k__1*[S]+K__2*[S^2])*ds/(V__max*[S])

 

"ⅆt = 1/(`V__max`*[S])+`k__1`/(`V__max`)+(`K__2`*[S])/(`V__max`)*ⅆs"

 

int(1/(V__max*S)+K__1/V__max+K__2*S/V__max, S = S .. S__0)

 

`assuming`([simplify(combine*(int(1/(V__max*S)+K__1/V__max+K__2*S/V__max, S = S__ .. S__0)), size)], [S > 0, S__0 > S__])

combine*piecewise(And(0 < S__0, S__ < 0), undefined, (1/2)*(K__2*S__0^2-K__2*S__^2+2*S__0*K__1-2*K__1*S__+2*ln(S__0)-2*ln(S__))/V__max)

 (1)

 

`assuming`([simplify(int(1/(V__max*S)+K__1/V__max+K__2*S/V__max, S = S__ .. S__0), size)], [S > 0, S__0 > S__])
  piecewise(And(0 < S__0, S__ < 0), undefined, (1/2)*(K__2*S__0^2-K__2*S__^2+2*S__0*K__1-2*K__1*S__+2*ln(S__0)-2*ln(S__))/V__max)NULL

 

 

maple*equation = manual*equation  NULL

(S__0^2*K__2-K__2*S^2+2*S__0*K__1-2*K__1*S+2*ln(S__0)-2*ln(S))/(2*V__max) = (ln(S__0/S)+K__1*(S__0-S)+(1/2)*(-S^2+S__0^2)*K__2)/V__max"(->)"false

   

eq1 := (S__0^2*K__2-K__2*S^2+2*S__0*K__1-2*K__1*S+2*ln(S__0)-2*ln(S))/(2*V__max)

 

eq2 := (ln(S__0/S)+K__1*(S__0-S)+(1/2)*(-S^2+S__0^2)*K__2)/V__max

 

eq1-eq2 = 0"(->)"false

 

(ln(S__0/S)+K__1*(S__0-S)+(1/2)*(-S^2+S__0^2)*K__2)/V__max = (ln(S__0/S)+K__1*(S__0-S)+(1/2)*(-S^2+S__0^2)*K__2)/V__max

 

Download mapleintvsmanualint.mw
Please Wait...