00:01
Right here we are going to be using the definition for the average value of a function over the given interval.
00:06
Well we are given a function f of x which is equal to the square root of x plus 2 and we are also given a closed interval.
00:14
The closed interval is from 1 to 13.
00:19
So the average value of the function over the interval from a to b is defined as 1 over b minus a times the integral from a to b of the function f of x dx.
00:34
So this is known as the average value of the function f of x over the closed interval from a to b.
01:01
So this is pretty much the formula that we are going to be using for this problem.
01:05
That's going to be in our case 1 over 13 minus 1 times the integral from 1 to 13.
01:13
Our function here is the square root of x plus 2 and then dx.
01:19
So that's going to be 1 over 12 times the integral from 1 to 13 of x plus 2 to the power of 1 half dx.
01:31
So here we can make a small u substitution.
01:33
For example, let u be equal to x plus 2.
01:41
Then du would equal to dx and therefore we are going to get the average value to be 1 over 12 times the integral.
01:49
We don't know the limits for the variable u...