Riemann Sums

A Riemann Sum uses rectangles to

• approximate the area under a curve. The more rectangles, the better the approximation.

• approximate the area under a curve. The less rectangles, the better the approximation.

• approximate the area under a curve. The more rectangles, the worse the approximation.

What does picture represent?

• Left Riemann Sum

• Right Riemann Sum

• Middle Riemann Sum

• Trapezoidal Sum

What is the value of the Riemann sum?

• 8

• 10

• 11

• 12

What does this picture represent?

• Left Riemann Sum

• Right Riemann Sum

• Middle Riemann Sum

• Trapezoidal Sum

Tags

CCSS.HSF.LE.B.5

What does this picture represent?

• Left Riemann Sum

• Right Riemann Sum

• Middle Riemann Sum

• Trapezoidal Sum

Tags

CCSS.HSF.LE.B.5

How would you describe the Reimann Sum shown in the picture?

• Overestimation of Area Under Curve

• Underestimation of Area Under Curve

• Exact Area Under Curve

• Choose this to get the wrong answer...

Based on the table, use a Left Riemann Sum and 4 sub-intervals to estimate the area under the curve. (Drawing a sketch of f(x) will help.)

• 5(3) + 1(4) + 2(5) + 1(7) = 36

• 5(4) + 1(5) + 2(7) + 1(6) = 45

• 5(3) + 6(4) + 8(5) + 9(7) = 142

• 0(3) + 5(4) + 6(5) + 8(7) = 106

Based on the table, use a Right Riemann Sum and 4 sub-intervals to estimate the area under the curve. (Drawing a sketch of f(x) will help.)

• 5(3) + 1(4) + 2(5) + 1(7) = 36

• 5(4) + 1(5) + 2(7) + 1(6) = 45

• 5(3) + 6(4) + 8(5) + 9(7) = 142

• 0(3) + 5(4) + 6(5) + 8(7) = 106

Use a Right Riemann Sum with 3 equal sub-intervals to approximate the area of the shaded area.

• 7

• 10

• 8

• 18

Use a Left Riemann Sum with 3 equal sub-intervals to approximate the area of the shaded area.

• 7

• 10

• 8

• 18