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

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.

Answer 1

[Torsten]

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.

[ByungChul Min]

Thank you very much