BATCH DISTILLATION :part 2(equilbrium y=(alpha*x)/((alpha-1)*x+1))
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part2 : Integral batch distillation.  
peter.vlasschaert@gmail.com , 18/02/2017

principle : integral

kill(all)$

eq1:'integrate(x^2,x)=integrate(x^2,x)+constant;

eq2:'integrate(x^2,x,a,b)=integrate(x^2,x,a,b);

equilibrium equation :' y '
alpha = relative volatility ( = constant )
info: https://en.wikipedia.org/wiki/Relative_volatility

eq11:y=(alpha*x)/(1+(alpha-1)*x);

A : alpha >  1

assume(x >= 0 and x <= 1);
assume(y >= 0 and y <= 1);
assume( alpha >1,b>a);
assume( a >0 and a < 1 and b < 1);

1e) integral for batch distillation.

eq22:op1='integrate(1/(rhs(eq11)-x),x,a,b);

alpha = value given.

eq23:ev(eq22,alpha=2.48);

integration values  a<b,a<1,b<1

eq24:ev(eq23,a=0.4,b=0.7);

eq25:ev(eq24,nouns);

=> ' op1 (= eq22) = op2 '
 input : alpha >1
        (begin = a,end = b of the interval for integration).

eq25:op2=integrate(1/(rhs(eq11)-x),x,a,b);

eq26:logcontract(eq25);

example : 

B : alpha = 2.1
    a     = .4
    b     = .7

eq26:ev(eq25,alpha=2.1,a=0.4,b=0.7);

alpha = 1 ? division by zero.