how can i write attached equation in MATLAB code

Answer 1

[Walter Roberson]

syms Delta_P_lo Delta_x phi_lo Delta_P_f x LB UB
Delta_P_f = Delta_P_lo * (1/Delta_x .* int(phi_lo.^2, x, LB, UB, 'hold', true))

Delta_P_f = 

The 'hold', true is there to prevent int() from immediately doing the integral. is independent of x so int() would treat it as being constant in x and would immediate do the integration, leaving you with something that did not include the integration sign.

If is dependent on x then the code would need to be changed a little to reflect that.

I had to introduce LB and UB as the bounds of integration because it happens that the 'hold' feature would be misinterpreted as being bounds if you were to try to do indefinite integration while 'hold' is on.

[NAVEED ULLAH]

First of all Thank for your detail answer and help.....

i would like to share , what actually i'm going to run... this is whole detail of equations

[Walter Roberson]

syms d g mu_1 mu_v rho_1 rho_v sigma chi
GAMMA = (rho_1/rho_v)^sym(1/2) / (mu_v / mu_1)^sym(1/8)

GAMMA = 

N_conf = 1/d * (sigma/ (g*(rho_1 - rho_v)))^sym(1/2)

N_conf = 

phi_lo__2 = 1 + (sym(4.3) * GAMMA^2 - 1) * (N_conf * chi^sym(7/8) * (1-chi)^sym(7/8) + chi^sym(1/8))

phi_lo__2 = 

syms Delta_chi Delta_P_f e_lo G L R

f_lo = (sym(0.79) * R * e_lo - sym(1.64))^(-2)

f_lo = 

Delta_P_lo = 2*f_lo * G^2 * L / (rho_1 * d)

Delta_P_lo = 

syms LB UB
Delta_P_f = Delta_P_lo * (1/Delta_chi .* int(phi_lo__2, chi, LB, UB, 'hold', true))

Delta_P_f = 

dPf = simplify(release(Delta_P_f))

dPf = 

Note that the Γ that shows up in the result is not the same as the Γ that you define at the bottom left of the equations. The one in the results is the Gamma function -- the extension of factorials.

[NAVEED ULLAH]

thank you very much.