Suppose that an object moving along a stra path has its velocity in feet per second at tin T seconds given by v(t) = (- 3)2 + 2. We will approximate this area by creating the sum by constructing four rectangles to appr the area. To create the midpoint sum you need to ev function at each of the midpoints of the sub On the graph, sketch the four rectangles wh you need to find. The enter the midpoints of
Suppose that an object moving along a stra path has its velocity in feet per second at tin T seconds given by v(t) = (- 3)2 + 2. We will approximate this area by creating the sum by constructing four rectangles to appr the area. To create the midpoint sum you need to ev function at each of the midpoints of the sub On the graph, sketch the four rectangles wh you need to find. The enter the midpoints of
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Creating the Midpoint Sum
Suppose that an object moving along a straight line
path has its velocity in feet per second at time t in
seconds given by v(t) =(- 3)? + 2.
We will approximate this area by creating the left-hand
sum by constructing four rectangles to approximation
the area.
To create the midpoint sum you need to evaluate the
function at each of the midpoints of the subintervals.
On the graph, sketch the four rectangles whose areas
you need to find. The enter the midpoints of each
interval below. Once your table is correct, the rest of the
problem will be revealed.
-2-
Interval [a,b]
Midpoint
Got it?
[2, 2.75]
2.375
You got it!
[2.75, 3.5]
3.125
You got it!
[3.5, 4.25]
3.875
You got it!
[4.25, 5]
4.625
You got it!
You got it! Now, fill out the table below, evaluating v(1)
at each midpoints and finding the area of each
rectangle.
Midpoint m
v(m)
Area
Got it?
2.375
Keep trying!
3.125
Keep trying!
3.875
Keep trying!
4.625
Keep trying!
What is the approximation of the area using the
midpoints?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52437306-811d-4520-b3b6-a71b3e8e7d5e%2F21e10d43-d65f-45af-86f7-6eeb36fb5ce8%2Fjmqm4fg_processed.png&w=3840&q=75)
Transcribed Image Text:Creating the Midpoint Sum
Suppose that an object moving along a straight line
path has its velocity in feet per second at time t in
seconds given by v(t) =(- 3)? + 2.
We will approximate this area by creating the left-hand
sum by constructing four rectangles to approximation
the area.
To create the midpoint sum you need to evaluate the
function at each of the midpoints of the subintervals.
On the graph, sketch the four rectangles whose areas
you need to find. The enter the midpoints of each
interval below. Once your table is correct, the rest of the
problem will be revealed.
-2-
Interval [a,b]
Midpoint
Got it?
[2, 2.75]
2.375
You got it!
[2.75, 3.5]
3.125
You got it!
[3.5, 4.25]
3.875
You got it!
[4.25, 5]
4.625
You got it!
You got it! Now, fill out the table below, evaluating v(1)
at each midpoints and finding the area of each
rectangle.
Midpoint m
v(m)
Area
Got it?
2.375
Keep trying!
3.125
Keep trying!
3.875
Keep trying!
4.625
Keep trying!
What is the approximation of the area using the
midpoints?
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