I want to integrate this function but I keep getting errors

Here is the code

func = @(initial) L/sqrt((E*I)/(2*F)) - integral(@(theta)1./sqrt(cos(initial)-cos(theta)),initial,pi/2);

OS = fsolve(func,0.5);

o = func(OS);

aa = linspace(0,pi);%X and Y of the theoredical

yy = @(aa) integral(cos(aa)/sqrt(cos(o)-cos(aa)),aa, pi/2);

All i need is for yy to get the values of the integration for all the values of aa. It keeps saying i need a function handle but then it thinks yy is a function, and doesnt compute it. i just need the intregal of the fuction from variable aa to pi/2.

Answer 1

[Star Strider]

Try something like this —

[L,I,E,F] = deal(rand,rand,rand,rand);                  % Use Correct Values

func = @(initial) L/sqrt((E*I)/(2*F)) - integral(@(theta)1./sqrt(cos(initial)-cos(theta)),initial,pi/2);
OS = fsolve(func,0.5);

Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.

o = func(OS)

o = 4.5196e-08

aa = linspace(0,pi);%X and Y of the theoredical 
yy = @(aa) integral(@(o)cos(aa)/sqrt(cos(o)-cos(aa)),aa, pi/2, 'ArrayValued',1);
YY = arrayfun(yy, aa);

Warning: Inf or NaN value encountered.

Warning: Inf or NaN value encountered.

figure
plot(aa, real(YY),  aa, imag(YY))
grid
legend('Real','Imag', 'Location','best')

.

[adam puchalski]

Yes this is very helpful thank you!!

[Star Strider]

My pleasure!

Answer 2

[Steven Lord]

yy = @(aa) integral(cos(aa)/sqrt(cos(o)-cos(aa)),aa, pi/2);

When you call this function handle it will attempt to evaluate the expression cos(aa)/sqrt(cos(o)-cos(aa)) expecting to obtain a function handle. If it does then it will pass that function handle into integral as the first input.

So I think what you want to do (if the integral is supposed to be computed over the variable o) is:

yy = @(aa) integral(@(o) cos(aa)/sqrt(cos(o)-cos(aa)),aa, pi/2);

[adam puchalski]

Yes you are right! Just need arguemnts at the end! thank you!