how to solve an equation where the unknown is an integration boundry for a numerical integration?

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David Welling 2020-4-19

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https://ww2.mathworks.cn/matlabcentral/answers/519076-how-to-solve-an-equation-where-the-unknown-is-an-integration-boundry-for-a-numerical-integration

回答： David Welling 2020-4-19

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I need to solve this equation in the form

for x where A is a constant and f a known function, which has to be integrated numerically.

However, when i define this function and try to solve, i get the error

"Error using integral (line 85)
A and B must be floating-point scalars."

Apparently I cannot put the variable I need to solve for in the boundry of the integral.

How can this be done?

Below is the code. I know, it is a lot of constants.

P_ep        = @(z) P_c.*(((exp(-(1/4).*(z./omega_c).^(5/12))).*((z./omega_c).^(3./2)))+(((4./C).*(2.84-0.92.*(1-cos(pi.*((sqrt(R.*z.*(z./(1.9.*omega_c)).^(0.14.*exp(23.*(S_y./E)))))./R))))).*(1-exp(-(1./25)*(z./omega_c).^(5./9))).*(z./omega_c)));  
syms        omega_m_ep
omega_m     = solve(integral(P_ep,omega_c,omega_m_ep) == (0.5 * m * V_1 ^2)- ((8/15)*E*sqrt(R)*omega_c^(5/2)),omega_m_ep);