Trapezoidal Method

Thread Starter


Joined Mar 19, 2009
Hi All,

I would like an answer checked that I have found for the following problem.

\( y = 5 \int^1_0 \frac{1}{1+x^2} dx \)


\( \int^1_0 f(x) dx = (b-a)[\frac{f(a)+f(b)}{2}] \)

\( 5*((1-0)*[\frac{{\frac{1}{1+0^2}+\frac{1}{1+1^2}}}{2}])\)

\(5*0.75 = 3.75\)

Have I solved this correctly?

I have tried to chack this in matlab with the code below but I am not getting this answer which now I am not sure which is incorrect.

X = 0:0.5:1;
Y = 5*(1./X.^2)
Z = trapz(X,Y)

Thanks for your time


Joined Feb 24, 2006
I think you are supposed to use more than a single trapezoid to approximate the integral. Did you really think one would do the trick?


Joined Mar 6, 2009
Plus your matlab code isn't correct.

For three terms it would be something like .... [I don't use Matlab]

Y=[5 5 5]./(1+X^2) ---- you missed the addition in your post

So to compare values for three terms, your pencil & paper method should have the sum of two trapezoidal approximations with limits from [0 to 0.5] and [0.5 to 1]

As Papbravo implies you should probably use several terms to come up with a good approximation to the 'exact' integral.


With 11 terms X=[0 0.1 0.2 .... 1.0] I get a value of Z=3.9249075
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