MATLAB: Matlab does not integrate

integrationMATLABsymbolic

why matlab don't integrate for my code?

Best Answer

Hi,

Your function is too much complex that int is unable to compute a closed form of indefinate integral. Numerical Integration will be more suitable for this function, but for that you will be evaluating definate integral.

If int cannot compute a closed form of an indefinite integral, try to approximate the expression around some point using taylor, and then compute the integral. For example, approximate the expression around t = 0. (Approximate Indefinite Integrals: https://www.mathworks.com/help/symbolic/int.html)

fApprox = taylor(f2, t, 'ExpansionPoint', 0, 'Order', 10);
int(fApprox,t)

Kindly check if you got some help from this.

Regards,

Abdulmanan Butt

Related Solutions

MATLAB: Integration in MATLAB with symbolic integration limits

syms x
y=x^2
f=int(y,1,x) % integration between 1 and x

MATLAB: How to create a symbolic function which fits the data so that I can use the symbolic INT function to double integrate

There are many possibilities to for computing A and the area of the hz shape:

1. You can use POLYFIT to calculate the coefficients of the desired polynomial function:

data = importdata('hz.data');
data = fliplr(data);
data(:, 1) = data(:, 1).*(pi/180);
p3 = polyfit(data(:,1),data(:,2),3);
% p3 = 
%      0.0053   -0.0740    0.2619    2.0549

Then you can use the coefficients to define your symbolic function:

syms r theta f
f =  0.0053*theta^3 - 0.0740*theta^2 + 0.2619*theta + 2.0549; % use values of p
A = eval(int(int(r,r,0, f), theta, 0, 2*pi))

2. You can use numerical approximation theory with DBLQUAD (as you requested a double integral) and INTERP1 to solve this issue:

data = importdata('hz.data');
data = fliplr(data);
data(:, 1) = data(:, 1).*(pi/180);
Ai = dblquad(@(r,theta) r.* (r <= interp1(data(:,1),data(:,2),theta,'spline')), 0, max(data(:,2)), 0, 2*pi)

3. You use POLYFIT with different orders (here as an example with order 3 and 7) instead of INTERP1:

data = importdata('hz.data');
data = fliplr(data);
data(:, 1) = data(:, 1).*(pi/180);
p3 = polyfit(data(:,1),data(:,2),3);
theta = 0:0.01:2*pi;
y3 = p3(1)*theta.^3 + p3(2)*theta.^2 + p3(3)*theta + p3(4);
A3 = dblquad(@(r,theta) r.* (r <= p3(1)*theta.^3 + p3(2)*theta.^2 + p3(3)*theta + p3(4)), 0, max(y3), 0, 2*pi)
p7 = polyfit(data(:,1),data(:,2),7);
y7 = p7(1)*theta.^7 + p7(2)*theta.^6 + p7(3)*theta.^5 + p7(4)*theta.^4 + p7(5)*theta.^3 + p7(6)*theta.^2 + ...
      p7(7)*theta + p7(8);
A7 = dblquad(@(r,theta) r.* (r <= p7(1)*theta.^7 + p7(2)*theta.^6 + p7(3)*theta.^5 + p7(4)*theta.^4 + ...
      p7(5)*theta.^3 + p7(6)*theta.^2 + p7(7)*theta + p7(8)), 0, max(y7), 0, 2*pi)

Best Answer

Related Solutions

MATLAB: Integration in MATLAB with symbolic integration limits

MATLAB: How to create a symbolic function which fits the data so that I can use the symbolic INT function to double integrate

Related Question