Math

Sequences & Series

2
Step 3
Consider the right endpoints approximation of the area of the region.
Observe the region between the graph of the function f(x) = 2x + 4 and the x-axis over the interval [0, 2]
with four circumscribed rectangles, which is shown below.
8
-0.5
0,5
1.0
1.5
2.0
2.5
The right endpoints of the n intervals are Ax(i) where i = 1 to
4
1
Then substitute Ax =
2
and n = 4 to find the left end points of four intervals.
1
Thus, the right end points of four intervals are Ax(i) =
(i), wherei = 1 to 4.
2
That is, the four right end points of the intervals are
1,
and 2.
2
Therefore, the four intervals are given as follows.
0 0
z] [
3
, 2]
2
2
Step 4
Using the right end points, the height of each rectangle is
1
122 [0]
.
where i = 1 to 4.
1
The width of each rectangle is
2
Step 5
Therefore, using the right end points, the sum of the areas of four rectangles is
4
1
2
2 - 2
i=1
Step 6
to approximate the sum of the area using right end points.
i=1
Simplify ] [173)
[
EL 913) - É O14:
04
4
Š
(3)
i=1
i=1
i=1
2
+ 1)
(3)
+
4
2
2
= 5+
Submit
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