00:01
In this question, given the values of the interval of f over the different limits of iteration, we are asked to calculate the interval from 8 to 9 of f x dx and the interval from 9 to 8 of 2f minus 6 d x.
00:17
The main formula we're going to use here, well, we're going to use two formulas, is that the interval from a to c, f of x dx dx, plus the interval from c to b, f of x dx dx, plus the interval from c to b, f of x dx, equals to the interval from from a to b f of x dx.
00:43
Here it's c not a.
00:48
And the second property we're going to use is the integral from a to b f of x dx equals to the negative interval from b to a f of x x x x.
01:04
Now, we want to get the interval from 8 to 9.
01:09
To get the interval from 8 to 9, we will first combine the intervals from 10 to 7 f of x d x plus the integral from 7 to 8 f of x d x note that the integral from 10 to 7 is the reverse of the interval from 7 to 10 so we can replace the integral from 10 first of all this equals to the interval from 10 to 8 by the previous property f of x d x and the inter we know the integral from 7 to 8 equals to 6 the integral from we know the integral from we know the interval from 7 to 10, therefore the interval from 10 to 7 is going to be negative 2 by the second property.
02:11
Since we know the interval from 7 to 10 to be 2, the interval from 10 to 7 is going to be negative 2, which means that the interval from 10 to 8 will be equal to 4, because negative 2 plus 6 equals to 4.
03:01
The negative of the interval from 10 to 8.
03:04
And we know that the interval from 10 to 8 equals to 4.
03:08
Therefore this will be equal to negative 4.
03:11
We know that the interval from 9 to 9 is going to be negative 6...