00:01
So in this question, they say i want to use a remon sum to approximate the area under the graph of f of x on the closed interval from 4 to 8 using n equals 4 sub -intervals and left endpoints.
00:14
We are going to draw the approximating rectangles.
00:19
So my first sub -interval is extending from x equals 4 to x equals 5.
00:28
Since i'm using a left remand sum from the left endpoint of that first sub -interval, x equals 4, i go up to the function, and over top of that sub -interval, i draw a rectangle whose height is given by the value of the function at that left endpoint.
00:54
My second sub -interval extends from x equals 5 to x -equals 6.
00:58
Again, i'm going to go to the left endpoint of that sub -interval, x equals 5.
01:07
And from that x value, i go up to the function, and over top of that sub -interval, i'm drawing a rectangle whose height is the y value at x -equals 5.
01:23
Third sub -interval goes from x -equal 6 to x -equal 7.
01:28
So again, i'm going to the left end point of that sub -interval, x -equals 6.
01:33
From there, i'm going up to the function, and i am drawing a rectangle over top of that sub -interval whose height is the value of the function at x -equal 6.
01:47
And then finally, my last sub -interval goes from x -equal 7 to x -equals 8...