00:01
Hi there, so for this problem, the information that we are given is that this function evaluated at 1 is equal to minus 1.
00:10
And this evaluated at 4 is equal to minus 4.
00:16
Now we are also given that the root of change of this function evaluated at 1 is equal to 2.
00:24
And yes, the derivative of this function evaluated at 4 is equal to minus 10.
00:31
Now we're told that the second derivative of this function is continuous, so we need to find the value of the following integral that will be from 1 to 4 of the border between x, and the second derivative of this function evaluated at x, integrated over x.
00:47
So to solve this integral, we need to use integration by pars.
00:51
So first of all, we're going to set that u is equal to x, so the differential in u is a differential in s, and the differential in b is the second derivative of this function.
01:05
Then if we integrate this, we will have that b is then just simply the first derivative of this function, okay? and then we can write this in the following way.
01:22
We can write now the integral as u times b.
01:27
So that will be x times the derivative of f of f, and evaluated then from 1 to 4, and this minus the integral of b times the differential in u, which is the differential in x...