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How can I solve an equation with variable in integral interval?

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ByungChul Min
ByungChul Min 2016-8-26
评论： ByungChul Min 2016-8-26
Hi, I am trying to solve a system of equations with variable in integral interval.
fun = @(x) x*normpdf(x);
f1: (1-normcdf(q,3,1))*p/(1+r) == c*(1-normcdf((c*q-equity)*(1+r)/p,3,1))
f2: (1-normcdf((c*q-equity)*(1+r)/p))*(1+r)*(c*q-equity)+p*integral(fun,0,(c*q-equity)*(1+r)/p) == (c*q-equity)
q and r are the variables and p, c, and equity are parameters. When I tried to solve this with vpasolve, it could not solve this probably because a variable is also in the integral interval.
Can anybody please help me with this problem? Thanks in advance.

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Torsten
Torsten 2016-8-26
You can give an analytical expression for your integral:
http://integrals.wolfram.com/index.jsp?expr=1%2Fsqrt%282*Pi%29%2Fs*Exp%5B-%28x-m%29%5E2%2Fs%5E2%5D*x&random=false
Best wishes
Torsten.

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