Area 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.

Based on the table, use a left Riemann sum and 4 sub-intervals to estimate the Area under the curve. (Choose the correct set-up.) 

• 5(3) + 1(4) + 2(5) + 1(7)

• 5(4) + 1(5) + 2(7) + 1(6)

• 5(3) + 6(4) + 8(5) + 9(7)

• 0(3) + 5(4) + 6(5) + 8(7)

• 14

• 9

• 10

• 5

Based on the table, use a Right Riemann sum and 4 sub-intervals to estimate the Area under the curve. (Choose the correct set-up.)

• 5(3) + 1(4) + 2(5) + 1(7)

• 5(4) + 1(5) + 2(7) + 1(6)

• 5(3) + 6(4) + 8(5) + 9(7)

• 0(3) + 5(4) + 6(5) + 8(7)

Approximate the area between the x-axis and h(x) = 1/7-x from x = 2 to x = 5 using a left Riemann sum with 3 equal subdivisions.

• 37/60 units²

• 47/60 units²

• 75/81 units²

• 3/5 units²

Approximate the area between the x-axis and h(x) = 1/7-x from x = 2 to x = 5 using a left Riemann sum with 3 equal subdivisions.

• 37/60 units²

• 47/60 units²

• 75/81 units²

• 3/5 units²

Approximate the area between the x-axis and f(x) = 2⁄x from x = 0.5 to x = 2 using a left Riemann sum with 3 equal subdivisions.

• 11/4 units²

• 11/3 units²

• 4 units²

• 3 units²

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.

Approximate the area between the x-axis and h(x) = 1/7-x from x = 2 to x = 5 using a left Riemann sum with 3 equal subdivisions.

• 37/60 units²

• 47/60 units²

• 75/81 units²

• 3/5 units²

What does picture represent?

• Left Riemann Sum

• Right Riemann Sum

• Middle Riemann Sum

• Trapezoidal Sum