00:01
Ok, so in this exercise we have our function f of x, and we need to compute the integral from 0 to 1 of f of x in the x.
00:12
Now, we can see that the region enclosed by the graph of our function and the x -axis on the interval 0 ,1, well, this region is just a trapezoid.
00:25
And what is the area of this trapezoid? well, here we are going to have the greater base, so 2, plus the smaller one, which is 1, divided by 2 and multiplied by the height of our trapezoid, which is 1.
00:44
So, we get 3 halves, which is 1 .5.
00:48
Perfect.
00:50
Now, let's compute the integral from 1 up to 8 of our function.
00:58
Well, the integral from 1 up to 8, to compute this one we can use a trick.
01:07
Let's observe that this integral can be written as the integral from 0 to 8, minus the integral from 0 to 1 that we have already computed.
01:21
Perfect.
01:22
Now, let's compute this integral.
01:24
Well, the integral from 0 to 8 of f of x in the x can be written as the integral from 0 to 2 of f of x in the x.
01:40
Perfect.
01:42
Plus the integral from 2 to 6 of f of x in the x, plus the integral from 6 to 8...