00:01
In your question, we want to find left and right point approximations for the area of this function over the interval 0 to 1.
00:08
What i'm going to first lay out is the values that we are working with here from 0 to 1.
00:16
So the x values that you've been told to use, starting at our left interval here, we would have 0, then 0 .25, then 0 .5, 0 .75, and 1.
00:41
The value of the function at those locations, what i'm going to write in the table is just plugging in those x values.
00:48
So this would be 0 times e to the 0.
00:52
The next one would be 0 .25 times e to the 0 .25.
00:58
The next one would be 0 .5 times e to the 0 .5.
01:05
0 .75 e to the 0 .75.
01:10
And then 1 times e to the first.
01:13
Now, you want to find a left estimate and a right estimate using four subintervals.
01:22
For the left estimate, that would be starting with the left boundary.
01:28
What we need to first understand is you're calculating rectangles, so we would have the value of the function, i'm going to put x sub i, times delta x.
01:41
Well, delta x in your problem is 0 .25, that's the amount of change in x, it's increasing by 0 .25 each time.
01:53
And that represents the width of the rectangle, and this represents our height.
02:00
For l4, your height is 0 times e to the 0, and we're multiplying that to our delta x 0 .25.
02:12
Then we would add our next rectangle height would be 0 .25 e to the 0 .25 times 0 .25.
02:27
Our next one would be 0 .5 e to the 0 .5 times 0 .25 for the width plus our last one...