Exploring Midpoint Sums and Riemann Sums

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

• y = x^2 - 1

• y = x^2 + 1

• y = x^3 + 1

• y = x^2 + 2

Into how many sections is the interval from x = -1 to x = 2 divided?

• 2 sections

• 3 sections

• 4 sections

• 5 sections

What is the width of each section when the interval is divided into three equal parts?

• 0.5

• 2

• 1

• 1.5

What is the height of the first rectangle using the midpoint method?

• 1/4

• 5/4

• 9/4

• 13/4

What is the total area approximation using the midpoint method?

• 5

• 13/4

• 8

• 23/4

What is the height of the first rectangle using the left endpoint method?

• 3

• 2

• 1

• 4

What is the total area approximation using the left endpoint method?

• 12

• 10

• 8

• 5

What is the height of the first rectangle using the right endpoint method?

• 1

• 2

• 3

• 4

What is the total area approximation using the right endpoint method?

• 5

• 8

• 10

• 12

What happens to the approximation as more rectangles with skinnier bases are added?

• It gets worse

• It stays the same

• It becomes exact

• It gets better