MATLAB: Integral from sin(x+y) from dx shows wierd result

integralsMATLAB

I have to integrate the function f = sin (x+y) giveing that a=0 and b = pi /2 ( the heads of the integral ) … the normal answer should had been sin(y) + cos(y) but my result is (2^(1/2)*sin(y + pi/4)) … I think the problem are the heads becouse if I simply do int(f,x) I get the right answer , but I put the head int(f,x,a,b) it show that weird result

Best Answer

Computers don't really care that YOU think it looks wierd. The fact is, that form for the integral is correct, just as much so as the solution that you like. It may depend on your MATLAB release, of course, since with R2019b, I get:

syms x y
>> int(sin(x+y),x,0,pi/2)
ans =
cos(y) + sin(y)

However, if we recognize the trig identity:

sin(u + v) = sin(u)*cos(v) + cos(u)*sin(v)

Now consider what happens if u = y, and v = pi/4. Then

sin(y + pi/4) = sin(y)*cos(pi/4) + cos(y)*sin(pi/4)

But sin(pi/4) = cos(pi/4) = sqrt(2)/2. Therefore you should see that

cos(y) + sin(y) = 2/sqrt(2) * sin(y + pi/4) = sqrt(2)*sin(y + pi/4)

Same answer. You may think it is wierd. But at least your release of the symbolic toolbox decided it was a simple form to report the solution. In fact, it arguably is simpler, in the sense there is only one term in the solution. The solution you got was entirely valid, as was the alternative. Getting into the mind of a computer is sometimes difficult to know why it may choose any specific form for the solution.

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MATLAB: Error using surf X, Y, Z, and C cannot be complex error

this is John BG <mailto:jgb2012@sky.com jgb2012@sky.com>

The problem is not in solving

x = 0:0.8:pi;
A = sin(x).^(1/3)
B = cos(x).^(1/3)

the operator

.^

solves for either real or complex.

The problem lays in the fact that surf doesn't take in complex values.

To solve the long expression of H, since you are dealing with complex numbers, you have to plot 2 surfs, not one: Real and Imaginary, or Modulus and Phase

clc
theta5=[0:0.1:pi];
theta4=[0:0.1:pi];
[X,Y]=meshgrid(theta4,theta5);
H=(((((cos(Y).^2-cos(X).^2-sin(X).^2+cos(X).^2.*sin(Y).^2+sin(X).^2.*sin(Y).^2).*(cos(X).^2.*cos(Y).^2-cos(X).^2*sin(X).^2+cos(Y).^2.*sin(X).^2+cos(X).^2.*cos(Y).^4.*sin(X).^2+2*cos(X).^2.*sin(X).^2.*sin(Y).^2-cos(Y).^2.*sin(X).^2.*sin(Y).^2-cos(X).^2.*sin(X).^2.*sin(Y).^4))./6+(cos(Y).^2-cos(X).^2-sin(X).^2+cos(X).^2.*sin(Y).^2+sin(X).^2.*sin(Y).^2).^3./27+(cos(X).^2.*cos(Y).^2.*sin(X).^2)./2-(cos(X).^2.*cos(Y).^6.*sin(X).^2)./2-(cos(X).^2.*cos(Y).^2.*sin(X).^2.*sin(Y).^2)./2-cos(X).^2.*cos(Y).^4.*sin(X).^2.*sin(Y).^2).^2-((cos(X).^2.*cos(Y).^2)./3-(cos(X).^2.*sin(X).^2)./3+(cos(Y).^2.*sin(X).^2)./3+(cos(Y).^2-cos(X).^2-sin(X).^2+cos(X).^2.*sin(X).^2+sin(X).^2.*sin(Y).^2).^2./9+(cos(X).^2*cos(Y).^4.*sin(X).^2)./3+(2.*cos(X).^2.*sin(X).^2.*sin(Y).^2)./3-(cos(Y).^2.*sin(X).^2.*sin(Y).^2)./3-(cos(X).^2.*sin(X).^2.*sin(Y).^4)./3).^3).^(1/2)-((cos(Y).^2-cos(X).^2-sin(X).^2+cos(X).^2.*sin(Y).^2+sin(X).^2.*sin(Y).^2).*(cos(X).^2.*cos(Y).^2-cos(X).^2.*sin(X).^2+cos(Y).^2.*sin(X).^2+cos(X).^2.*cos(Y).^4.*sin(X).^2+2.*cos(X).^2.*sin(X).^2.*sin(Y).^2-cos(Y).^2.*sin(X).^2.*sin(Y).^2-cos(X).^2.*sin(X).^2.*sin(Y).^4))./6-(cos(Y).^2-cos(X).^2-sin(X).^2+cos(X).^2.*sin(Y).^2+sin(X).^2.*sin(Y).^2).^3./27-(cos(X).^2.*cos(Y).^2.*sin(X).^2)./2+(cos(X).^2.*cos(Y).^6.*sin(X).^2)./2+(cos(X).^2.*cos(Y).^2.*sin(X).^2.*sin(Y).^2)./2+cos(X).^2.*cos(Y).^4.*sin(X).^2.*sin(Y).^2).^(1/3)+cos(X).^2./3-cos(Y).^2./3+sin(X).^2./3+((cos(X).^2.*cos(Y).^2)./3-(cos(X).^2.*sin(X).^2)./3+(cos(Y).^2.*sin(X).^2)./3+(cos(Y).^2-cos(X).^2-sin(X).^2+cos(X).^2.*sin(Y).^2+sin(X).^2.*sin(Y).^2).^2./9+(cos(X).^2.*cos(Y).^4.*sin(X).^2)./3+(2*cos(X).^2.*sin(X).^2.*sin(Y).^2)./3-(cos(Y).^2.*sin(X).^2.*sin(Y).^2)./3-(cos(X).^2.*sin(X).^2.*sin(Y).^4)./3)./(((((cos(Y).^2-cos(X).^2-sin(X).^2+cos(X).^2.*sin(Y).^2+sin(X).^2.*sin(Y).^2).*(cos(X).^2.*cos(Y).^2-cos(X).^2.*sin(X).^2+cos(Y).^2.*sin(X).^2+cos(X).^2.*cos(Y).^4.*sin(X).^2+2.*cos(X).^2.*sin(X).^2.*sin(Y).^2-cos(Y).^2.*sin(X).^2.*sin(X).^2-cos(X).^2.*sin(X).^2.*sin(Y).^4))./6+(cos(Y).^2-cos(X).^2-sin(X).^2+cos(X).^2.*sin(Y).^2+sin(X).^2.*sin(Y).^2).^3./27+(cos(X).^2.*cos(Y).^2.*sin(X).^2)./2-(cos(X).^2.*cos(Y).^6.*sin(X).^2)./2-(cos(X).^2.*cos(Y).^2.*sin(X).^2.*sin(Y).^2)./2-cos(X).^2.*cos(Y).^4.*sin(X).^2.*sin(Y).^2).^2-((cos(X).^2.*cos(Y).^2)./3-(cos(X).^2.*sin(X).^2)./3+(cos(Y).^2.*sin(X).^2)./3+(cos(Y).^2-cos(X).^2-sin(X).^2+cos(X).^2.*sin(Y).^2+sin(X).^2.*sin(Y).^2).^2./9+(cos(X).^2.*cos(Y).^4.*sin(X).^2)./3+(2.*cos(X).^2.*sin(X).^2.*sin(Y).^2)./3-(cos(Y).^2.*sin(X).^2.*sin(Y).^2)./3-(cos(X).^2.*sin(X).^2.*sin(Y).^4)./3).^3).^(1/2)-((cos(Y).^2-cos(X).^2-sin(X).^2+cos(X).^2.*sin(Y).^2+sin(X).^2.*sin(Y).^2).*(cos(X).^2.*cos(Y).^2-cos(X).^2.*sin(X).^2+cos(Y).^2.*sin(X)^2+cos(X).^2.*cos(Y).^4.*sin(X).^2+2.*cos(X).^2.*sin(X).^2.*sin(Y).^2-cos(Y).^2.*sin(X).^2.*sin(Y).^2-cos(X).^2.*sin(X).^2.*sin(Y).^4))./6-(cos(Y).^2-cos(X).^2-sin(X).^2+cos(X).^2.*sin(Y).^2+sin(X).^2.*sin(Y).^2).^3./27-(cos(X).^2.*cos(Y).^2.*sin(X).^2)./2+(cos(X).^2.*cos(Y).^6.*sin(X).^2)./2+(cos(X).^2.*cos(Y).^2.*sin(X).^2.*sin(Y).^2)./2+cos(X).^2.*cos(Y).^4.*sin(X).^2.*sin(Y).^2).^(1/3)-(cos(X).^2.*sin(Y).^2)./3-(sin(X).^2.*sin(Y).^2)./3;
figure(1);surf(X,Y,abs(H))
figure(2);surf(X,Y,angle(H))

if you find this answer useful would you please be so kind to consider marking my answer as Accepted Answer?

To any other reader, if you find this answer useful please consider clicking on the thumbs-up vote link

thanks in advance for time and attention

John BG

<mailto:jgb2012@sky.com jgb2012@sky.com>

MATLAB: I need to write a script for a nonlinear system equations.

Example:

syms x y
eqn1 = cos(x) - sin(y) == 1/10
eqn2 = sin(x) + 3 * cos(y) == 2
solve(eqn1, eqn2)

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MATLAB: Error using surf X, Y, Z, and C cannot be complex error

MATLAB: I need to write a script for a nonlinear system equations.

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