how to solve definite integral where the limits itself contain the variable to be integrated and also without using iteration method.

%finding Id without iteration
clc
epsi = 12.47*10^-12*8.85;
Dd = 5*10^-9;
Di = 5*10^-9;
a = 0.125*10^-20*1.6*10^-19;
z = 100*10^-6;
Vs = 2.63*10^5;
G0 = (q^2*epsi*z*Vs)/(q^2*(Dd+Di)+epsi*a);
Vg = 0;
Vt = -0.485;
Rs = 12;
Rd = 12;
Vd = 0;
t0 = Id/(G0*(Vg-Vt-Id*Rs));
t1 = Id/(G0*(Vg-Vt-Vd+Id*Rd));
mu = 0.93;
L = 100*10^-9;
A = -(Vs*L*G0)/mu;
r = integral(@(t)1./(t.^2.*log(1-t)),t0,t1);
Id=A/r

[Walter Roberson]

q is not defined.

[Torsten]

Id is defined too late.

And what do you mean by "where the limits itself contain the variable to be integrated" ?

In the case you provided, the limits are constant fixed values.

[neetika sharma]

actually we need to calculate Id which is in the limits t0 and t1. is it possible to solve without giving initial guess value of Id?

[Walter Roberson]

No, it will not be possible.

Answer 1

[Walter Roberson]

If the limits of a 1 dimensional integral contain the variable to be integrated over, then you do not have a definite integral and you cannot solve the problem with a numeric integration.

1/(t^2*log(1-t)) does not have any obvious closed form solution, so unless you can research and find a formula for it, you will need to work numerically -- which would require that you had numeric values for q and Id.