You may be able to compute the upper limit as follows:
1) Compute the indefinite integral of the expression y.*z
>> syms x
>> h = 1.0545718E-34;
>> g = 5.344285879E-28;
>> C = 1/sqrt(2.*pi);
>> y = (C - (exp(2.*g.*i.*x./h)).*(C - cos(x).*((h.^2)./2) + (g.*x)/2.*h.*i));
>> z = (C - (exp(-2.*g.*i.*x./h)).*(C - cos(x).*((h.^2)./2) + (g.*x)/2.*h.*-i));
>> out = int(y.*z);
This returns a symbolic expression 'out' as a function of x
2) Write this as an equation which we would like to solve:
3) The value of out in the lower bound (0) is 0 which can be verified by
Therefore, we can solve for the upper bound as follows:
>> solx = solve(eqn,x)
>> x = (2*pi)/solx;
4) Verify the output:
>> out1 = int(y.*z,0,(2.*pi)./x);
>> double(out1)
ans =
1
Best Answer