Using Trapz in matlab

Estimate the following integral using the trapz matlab function and b) the matlab function quad. Use n=2,4,8,16,32,64,128 and plot the difference bewtween the two methods as a function of n.

The function is as follows. sqrt(x)./(x+2)dx 1<=x<=3

So i am able to comfortable get the quad. However I can't seem to get a value for trapz. Here is what I have tried

First I made a for loop, Since I know that trapz operates on data not functions.

for k=1:7 y=2.^k end

However I'm not sure how to implement the for loop into solving the integral.

also how would I plot the difference bewtween the two methods as a function of n. I don't even understand what that means.

Thanks for the help

Answer 1

[Youssef Khmou]

hi, Brandon

In this example you have to use function handle ,so what i understand is that you need to see when the two methods are equal. Here is a proposition :

1) You create a function handle :

 f=@(x) sqrt(x)./(x+2);

2) You create the the number of spacing elements on which Trapz method wil be evaluated :

 n=2.^(1:7); %

3) You initialize the vectors that will contain the numercial intergations :

 I1=zeros(1,7);
 I2=zeros(1,7);

4) You implement a loop : ! YOU have to complete the two lines

 for ii=1:length(n)

    x=linspace(1,3,n(ii));

    I1(ii)=quad(f,...... % INCOMPLETE LINE 
    I2(ii)=trapz(x,..... % INCOMPLETE LINE 

 end

Now you can see when the two methods are equal .

 figure, plot(n,I1); hold on, plot(n,I2,'r'),legend('QUAD','TRAPZ')

[Brandon]

Hi I appreciate the response and explanation. However the only thing you failed to answer was my question on how to use trapz properly. I'm really struggling with that.

Thanks!

[Youssef Khmou]

ok fine: " I2(ii)=trapz(x,f(x));" if you use "trapz(f(x))" the Integral is evaluated with default spacing : one, but with the first formula " trapz(x,f(x))" you impose on the function to eval the Integral on the specified x Axis , and our x Axis increases in sampling in the loop and then convereges to QUAD .