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Unable to solve a double integration

Posted 10 years ago

I have been using Mathematica 9 to solve a double integration (Equation 1) but without any success. enter image description here

I was told that the value of $\alpha$ will be 0.2826 when the following data is used for the constants: enter image description here

I uses NIntegrate but still can't obtain 0.2828 for the $\alpha$ value. I am not sure if i have the code wrong and hope someone in the community can help.

POSTED BY: kok wong
6 Replies
Posted 10 years ago

Could you possibly use the exact value of the indefinite integral to help trying to find your solution

In[1]:= lmean = 8814/10^4;
lc = 5613/10^4;
Af = 12/10;
u = 1/10;
a = 10813/10^4;
b = 12/10;
p = 1;
q = 25294/10^4;
lct[t_] := lc*(1 - A*Tan[t])/(Exp[u*t]);
f[l_] := a*b*l^(b - 1)*Exp[-a*l^b];
g[t_] := ((Sin[t])^(2*p - 1)*(Cos[t])^(2*q - 1))/(Integrate[(Sin[w])^(2*p - 1)*(Cos[w])^(2*q-1), {w,0,Pi/2}]);
FullSimplify[Integrate[f[l]*g[t]*(l/lmean)*(l/(2*lc))*Exp[u*t], l], Assumptions -> 0 <= t < 2 Pi && 0 <= l]

Out[12]= -(1/2407281094647)126470000 E^(-((10813 l^(6/5))/10000) + t/10) l^(4/5) Cos[t]^(10147/2500)
    (150000 + 97317 l^(6/5) + 100000 E^((10813 l^(6/5))/10000)ExpIntegralE[1/3, (10813 l^(6/5))/10000]) Sin[t]

In[13]:= FullSimplify[Integrate[f[l]*g[t]*(l/lmean)*(l/(2*lc))*Exp[u*t], t, l],
   Assumptions -> 0 <= t < 2 Pi && 0 <= l]

Out[13]= -(1/(Cos[t]^(2353/2500)))(2470117187500/892485605516233971387177524702941121272167 -
    (1788364843750 I)/68652738885864151645167501900226240097859) E^(-((10813 l^(6/5))/10000) +
    (1/10 - I) t) (1 + E^(2 I t)) l^(4/5) (150000 + 97317 l^(6/5) + 100000 E^((10813 l^(6/5))/10000)
    ExpIntegralE[1/3, (10813 l^(6/5))/10000]) (1243209104158084056000 E^(I t)
    Hypergeometric2F1[2647/5000 - I/20, 1, 7353/5000 - I/20, -E^(2 I t)] - (250 + 2353 I)
    (51882557652852180070 Cos[t] + 26149933547065465035 Cos[3 t] + 5233573221864243007 Cos[5 t] - 
    250 (19936133122065382 Sin[t] + 7069109 (485993763 Sin[3 t] + 58539109 Sin[5 t]))))

If I include A=1 then I get a ConditionalExpression depending on (1 - Tan[t])^(2/5)>0 for the exact definite integral for l. For a few other values of A I get a string of "PolynomialGCD::lrgexp: Exponent is out of bounds for function PolynomialGCD." and no result.

POSTED BY: Bill Simpson
Posted 10 years ago

Thanks Marco for your comment.

Not sure if the integrand can be solved or not.

POSTED BY: kok wong
POSTED BY: Marco Thiel
Posted 10 years ago
POSTED BY: kok wong
Posted 10 years ago

Eqn 1 is separated into two sections and notebooks are attached.

Attachments:
POSTED BY: kok wong

It will be a good idea if you publish the notebook showing what you have tried so far.

POSTED BY: Jose Calderon
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