"Trapz" function gives result different than what I calculate by hand

0

I'm trying to remember how the trapz function works by doing a little manual test on the console:

>> x=linspace(1,5,5)

x =

1 2 3 4 5

>> y=x

y =

1 2 3 4 5

>> trapz(x,y)

ans =

12

However, when I try this example using pen and paper I get this: I=(1+0)x1/2 + (2+1)x1/2 + (3+2)x1/2 + (4+3)x1/2 =0.5 + 1.5 + 2.5 + 3.5 = 8

In the above calculation, I did the sum of the aereas of 4 trapezoids, the first one having the bigger base equal to 1 and the little base equal to 0, the second one having the bigger base equal to 2 and the little base equal to 1, etc.

To test the correctness of my pen-and-paper calculation, I did another example with different arrays:

>> x=linspace(0,5,6)

x =

0 1 2 3 4 5

>> y=x

y =

0 1 2 3 4 5

>> trapz(x,y)

ans =

12.5000

Then I calculated with pen and paper:

I=(1+0)x1/2 + (2+1)x1/2 + (3+2)x1/2 + (4+3)x1/2 + (5+4)x1/2 = 0.5 + 1.5 + 2.5 + 3.5 + 4.5 = 12.5

What am I missing?

Answer 1

[Torsten]

For x = y = [1 2 3 4 5],

I = (1+2)/2 + (2+3)/2 + (3+4)/2 + (4+5)/2 = 24/2 = 12.

[Abdallah]

Yup, I figured out my mistake: I was calculating the areas of the trapezoids not from y=0 but from y=1, which isn't how integrals work.