00:01
So in this question, they say use the method of midpoint rectangles to approximate the area under the curve f of x, which is equal to x squared plus 2x plus 5, from x equals 3 to x equals 33, and we're going to use n equals five rectangles to find our approximation.
00:19
So they are telling us that we are taking an interval from 3 to 33, and we're breaking it up into five subintervals.
00:32
Of equal width.
00:34
Now, the distance from x equals 3 to x equals 33 is 30.
00:41
So that means each of my subinterrals has a width of 30 divided by 5, which is 6.
00:49
So my first sub interval goes from 3 to 9.
00:53
My second one, 9 to 15.
00:57
My third one, 15 to 21.
01:01
My fourth one, from 21 to 27.
01:05
And my last one, from 27 to 33.
01:09
So what do we do? we take the width of each of these rectangles, which is going to be six, and i multiply by the height of the function at the midpoint of that sub -edable.
01:26
So in this case, i'm getting 6f of 6 as the area of my first rectangle.
01:34
My second rectangle, its midpoint is xx.
01:39
Equals 12...