00:01
We want to approximate the value of the interval from 0 to 4 of 2 raised to the x by the trapezoidal rule with 12 sub -intervals.
00:11
For that, we start by defining the function f of x equal 2 -raise to the x, and we consider that function defined on the close interval 0, 4.
00:27
Now we calculate the step size h, which is the common distance, any two consecutive nodes and is defined as the length of the interval of integration 4 minus 0 over the number of sub -intervals 12 in this case this gives us 4 over 12 which is 1 third so each is 1 3rd with this we can now calculate the nodes will be using any node x of i is given us 0 the left -hand point of the interval of integration plus i times h.
01:08
That is i times one -third or i over 3.
01:15
And the index i goes from the value 0, 1 up 2, up to 12.
01:29
And with this we can now say that the interval from 0 to 4 of 2 raised to the x is approximately equal.
01:40
To t12, that is the trapezo is a rule with 12 subintervals, which is defined as each half times the image of the first node x0 plus two times the sum of the images of the internal nodes, that is, from index i1 to 11, plus the image of the last node x12...