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how can i get this results?

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sajjad barzigar
sajjad barzigar 2021-2-26
关闭： John D'Errico 2021-3-20
i wrote this code to solve the integral shown in the picture and i should get the result as shown in the picture(equation 39):
this is the code that i wrote:
clc
clear all
close all
%--------------------------------------------------------------------------
syms Alpha1 Betta2 Betta1 S1 S2 h t R h H STRp m
%______________________________________________________________________________
PART1=(STRp)*(2*pi)*(R);
Eint_AB1=int(int(-S1*PART1,S1,(m*h)/cos(Alpha1),h),Alpha1,acos(m),0)
%________________________________________________________________
PART2=(STRp)*(2*pi)*(R);
Eint_BC1=int(int((-S1*PART2),S1,0,h),Betta1,pi/2,acos(1-m))
%____________________________________________________________________________________
PART3=(STRp)*(2*pi)*(R);
Eint_BC2=int(int((-S2*PART3),S2,0,((1-m)*h)/cos(Betta2)),Betta2,acos(1-m),0)
%______________________________________________
E_int=Eint_AB1+Eint_BC1+Eint_BC2
this is the answer that i get:
Eint_AB1 =
int(-(pi*R*STRp*h^2*(cos(Alpha1)^2 - m^2))/cos(Alpha1)^2, Alpha1, acos(m), 0)
Eint_BC1 =
R*STRp*h^2*pi*(pi/2 - acos(1 - m))
Eint_BC2 =
int(-(pi*R*STRp*h^2*(m - 1)^2)/cos(Betta2)^2, Betta2, acos(1 - m), 0)
E_int =
int(-(pi*R*STRp*h^2*(m - 1)^2)/cos(Betta2)^2, Betta2, acos(1 - m), 0) + int(-(pi*R*STRp*h^2*(cos(Alpha1)^2 - m^2))/cos(Alpha1)^2, Alpha1, acos(m), 0) + R*STRp*h^2*pi*(pi/2 - acos(1 - m))
E_int is the results which should be equal to equation 39 in the picture but i get the results from matlab in the form of integral.how should i write this code to get the results as the equation 39 in the picture?
how can i solve this problem?

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