00:01
Hey folks, so we're working with this function, y equals square root x plus one.
00:06
We're trying to do remand sums with the given partition.
00:11
So it looks like we're going from zero out to two, and we have eight rectangles.
00:19
So the width of each rectangle, delta x, is going to be, well, one -fourth, right? which is the same thing as taking the total width and then dividing it up into we want eight rectangles, right? so that's the same thing as one fourth.
00:41
And so the upper sum is going to be the one where we take right end points.
00:50
So the right remon sum, i'll call it r.
00:54
We'll be using right endpoints.
00:56
As we can see from the picture.
00:58
That's how we get an overestimate.
01:01
And so this will be the delta x times then, well, we just need to plug in all of the values to this.
01:11
In the end, i'm going to get plus one.
01:13
This plus one is going to show up eight times, right? so i'll just go ahead and put an eight.
01:19
And then plus, when i plug in each of the values, so it'll be square root of a fourth, square root of two -fourths, which is one -half, square root of three -fourths, square root of one, which is just, i'll just write it, square root of five -fourths, square root of six -fourths, which simplifies to three halves, square root of seven -fourths, and then finally, square root of two is the last one, these right end points, close -print.
01:58
You can go ahead and figure that out by plugging it into a calculator to get an approximation...