Hi, I think I'm average on the trapezoidal rule right now, but there is one thing I'm a bit confused about.
Ok so I know the trapezoidal rule is a∫bf(x)dx=(b-a)/2n [f(x0) + 2f(x1) and so on]
Though I'm a bit confused on it.
I'll give some examples:
0∫2x3dx, n=4, so I know that it moves up 1/2 each up
So it's like this (2-0)/2(4)[0+2(1/2)3 until (2)3], I know the answer to this, but I was wondering why does it start off with 0
Another example is:
1∫2(1/(x+1)2) dx, n=4, and it starts off with (1/4) + 2(1/(5/4)+1)2) and so on
Like here I'm a bit confused why it starts off with 1/4, when n is equal to 4, but then it goes up to 5 things inside the brackets [ ]
Like it started with 1/4 by itself, then went onto the function with 5/4, so can someone explain how does it start off exactly.
One more example is:
0∫1√x√(1-x) dx, n=4, and the change in x is 1/4
But it starts off with 0 + 2√(1/4)(1-1/4) and so on...
So yeah, I know that after the starting thing inside the bracket goes through the pattern, but I was wondering how does it start off. At first I just though it started off with the pattern, but when I saw like the 3rd example started off with a 0, then went onto x1 then x2 then x3, etc.