field radiation pattern generation

please help me in writing code for attached file. i have written code like below but it is taking many hours for execution. so please help me for fast execution of equation in the attached file.

code i have written is

theta=[-90:0.01:90];
syms x
L=5;
A(x)=sym(1-(2*x/L)^2);
A(x)=(1-(2*x/L)^2);
phi(x)=sym(0)
phi(x)=0;
u=sin(theta);
fun=(A(x)*(exp((j*pi*10)*((u*x)+phi(x)))));
E= int(fun,x,-1,1)
Edb=20*log10(E);
plot(u,Edb);
grid on
title("radiation pattern");

help me what modifications i have to do for fast execution of this code

[Image Analyst]

Does it have to be symbolic, or can we do it numerically where you define some range for your input?

[darova]

@ramya k comment's moved here

we have to write numerically and we should get plot for that

please verify the attached file.. in that electric field equation available.. we have to execcute that equation.

Answer 1

[darova]

Use trapz

t = -90:90;         % i choosed step 1
x = -1:0.1:1);
[T,X] = meshgrid(t,x);
u = sin(T);
A = ...%
fun = A.*exp(...);
E = trapz(x,fun,1);
plot(t,E)

[ramya k]

tq for your idea, but i didnt get proper pattern, i got some scattered pattern when wrtten code according to your idea. i have uploaded required model pattern and what i got now. i am very new the matlab so please help me.

[darova]

please attach the code

[ramya k]

please find the code

[darova]

Range of X axis is [-1 1] here. BUt it's impossible since it's range of (x is integration variable, it disappears after integration)

The code and formulas are also not identical. but you assumed A=1 in your code

Can you collaborate?

[ramya k]

A means amplitude, it can be anything like constant or circle or parabola. thats y i have taken constant as 1 in first execution.

[darova]

i made some correction to your code

clc,clear

t = -90:90;        
x = -1:0.1:1
[T,X] = meshgrid(t,x);
u = sin(T);
A = 1;
phi = 0;
fun = A.*exp(1j*pi*10*(u.*X+phi));
E = trapz(X,fun,1);
Edb = 20*log10(E);
plot(t,E)

[ramya k]

thank you so much for your help