00:01
All right, so i've taken the liberty of doing two things here.
00:05
I've written out all of the values that we have for the cross -sectional areas over here on the left side.
00:10
Then i have also written out there are midpoints here in the second column.
00:16
And remember that to find the midpoint, we just add, we just take the average of these two values.
00:21
So 0 plus 18 over 2 equals 9 and then 18 plus 58 over 2 equals 38.
00:25
And we did that for all of these.
00:28
It's rather time -consuming, but this is going.
00:30
Going to be the result.
00:33
After that, what the midpoint rule tells us is that in order to approximate the volume here, we're going to need to take 1 .5, which is the distance between the cross sections, and we multiply 1 .5 by 9, which is one midpoint, then add to that 1 .5 times 38, then add to that 1 .5 times 68 .5, etc.
00:58
And we can also do something somewhat, simpler, which is first we add all of these midpoint values, and then we multiply by 1 .5.
01:06
We just distribute out the 1 .5.
01:14
So if you add up all of these midpoints, you can do this by hand.
01:18
I wouldn't recommend it...