Riemann Sum Area Approximations

The video tutorial explains how to approximate the area between the x-axis and a function graph using a right Riemann sum with three equal subdivisions. It begins by setting up the problem with given values and drawing axes. The instructor plots points and discusses possible shapes of the function. The tutorial then calculates the Riemann sum by defining the height of rectangles using the right boundary of each subdivision. Finally, it concludes with the approximation of the area and discusses the potential accuracy of the approximation.

What is the purpose of using a right Riemann sum in this context?

• To calculate the slope of the curve

• To approximate the area under the curve

• To find the exact area under the curve

• To determine the function's maximum value

How many subdivisions are used in the right Riemann sum for this problem?

• Three

• Five

• Four

• Two

What information is provided to help approximate the area under the curve?

• The integral of the function

• A table of values for the function

• A complete graph of the function

• The derivative of the function

Which of the following is true about the function's behavior between data points?

• The function is linear between points

• The function's behavior is unknown between points

• The function is constant between points

• The function is quadratic between points

What is the width of each subdivision in the right Riemann sum?

• 4

• 3

• 1

• 2

How is the height of each rectangle determined in a right Riemann sum?

• Using the right boundary of each subdivision

• Using the average of the left and right boundaries

• Using the midpoint of each subdivision

• Using the left boundary of each subdivision

What is the height of the rectangle for the first subdivision?

• 6

• 5

• 3

• 8

What is the total area approximation using the right Riemann sum?

• 36

• 42

• 54

• 48

Which factor could affect the accuracy of the Riemann sum approximation?

• The color of the graph

• The type of paper used

• The speed of calculation

• The number of subdivisions

What is the height of the rectangle for the third subdivision?

• 5

• 3

• 8

• 6