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

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Abdallah
Abdallah 2022-8-2
编辑： Abdallah 2022-8-2
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?

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回答（1 个）

Torsten
Torsten 2022-8-2
For x = y = [1 2 3 4 5],
I = (1+2)/2 + (2+3)/2 + (3+4)/2 + (4+5)/2 = 24/2 = 12.
  1 个评论
Abdallah
Abdallah 2022-8-2
编辑：Abdallah 2022-8-2
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.

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