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Exploring Midpoint Riemann Sums in Calculus

Exploring Midpoint Riemann Sums in Calculus

Assessment

Interactive Video

•

Mathematics

•

6th - 10th Grade

•

Practice Problem

•

Hard

Created by

Ethan Morris

FREE Resource

The video tutorial explains how to approximate the area under the curve f(x) = x^2 from 0 to 1 using the midpoint rule with four equally spaced subintervals. It covers calculating Delta X, constructing rectangles at midpoints, determining rectangle heights, and computing the total area. The tutorial also compares the midpoint rule with other methods, highlighting that the average of left and right sums does not equal the midpoint sum.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the function used in the video to approximate the area under the curve?

y = x^3

y = 1/x

y = x^2

y = sqrt(x)

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the interval over which the area is being approximated?

[0, 2]

[1, 2]

[0, 1]

[0, 0.5]

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How many sub-intervals are used in the midpoint rule for this problem?

2

3

5

4

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of Delta X for the given problem?

1/2

1/5

1/3

1/4

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which point is used to construct the rectangles in the midpoint rule?

Right endpoint

Any point

Left endpoint

Midpoint

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the midpoint of the first sub-interval [0, 1/4]?

3/8

1/4

1/8

1/2

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the height of the rectangle at the midpoint 3/8?

f(7/8)

f(3/8)

f(5/8)

f(1/8)

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