trapz Vs. quad - 1 integral 2 different results

Hi every one,

I'm trying to find a numeric solve for an integral, and got some weird answer.

so i tried with another function and got a different answer.

i suppose one of them is the right answer, my bet is the trapz answer is the right one. but I'm not sure.

can somebody explain where i am wrong? next thing i need to solve an 2d-integral using quad2d, and i have to know how to do it right.

10x

here is a running code:

 clear
 Fi1=@(ro,z,theta1,k)exp(k.*z.*cos(theta1).*1i).*sqrt(cos(theta1)).* sin(theta1).^2.*besselj(1.0,k.*ro.*sin(theta1));

 NA=0.95;
 ni=1;
 alpha=asind(NA/ni)
 alpha=asin(NA/ni);

 lambda=600e-9;

 r=0.5e-6;
 z=0;
 V=linspace(0,alpha,300);
 k=2*pi/lambda;

 I1_1=trapz(  Fi1(r,z,V,k), V)
 I1_2=quad( @(theta1)  Fi1(r,z,theta1,k),  0,alpha)

Answer 1

[Marlies]

• The practical answer to why you get two different answers is that you have switched the X- and Y input for the trapz command. If you replace the line that computes I1_1 with the line below, you will get the same answer for the two.

I1_1=trapz(V, Fi1(r,z,V,k))

• The more generic question is which integration-command you should be using to solve a 2D integral. Of the two methods you mentioned, only quad2d is capable of performing 2D quadratic integration.
• If you also have access to release R2012a, there is also the command 'integral' available. That command uses a global adaptive quadrature while quad uses the adaptive Simpson quadrature (1D) or integration over the planar region (2D). See also the documentation for those two methods: href=""<http://www.mathworks.com/help/techdoc/ref/f16-5872.html#f16-6472</a>>

Hope this helps.

Marlies