Approximate Areas with Riemann Sums

Use 3 trapezoids to determine the approximate area of the shaded area.

• 12

• 9

• 10

• 5

Based on the table, use a trapezoidal sum of 4 sub-intervals to estimate the area under the curve. (calculator allowed for arithmetic)

• 32.5

• 40.5

• 78

• 160

• 100

• 200

• 400

• 60

Find the right-hand Riemann Sum, with three sub-intervals indicated by the table.

• 28

• 16

• 34

• 23

Find the Left-hand Riemann Sum, with three sub-intervals indicated by the table.

• 28

• 16

• 34

• 23

Set up the area under y = h(x) from x = -2 to x = 4 using a Left Riemann Sum and three equal sub-intervals.

• -2(0) + 0(4) + 2(6)

• 2(4) + 2(6) + 2(4)

• 2(0) + 2(4) + 2(6)

• 2(1) + 2(5.5) + 2(5.75)

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

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

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What kind of Riemann sum is described by the diagram?

• Left-hand

• Right-hand

• Midpoint

We're interested in calculating the area under the curve for x between -6 and 6. Order the areas from LEAST to GREATEST.

• left-hand, right-hand, midpoint

• right-hand, left-hand, midpoint

• right-hand, midpoint, left-hand

• left-hand, midpoint, right-hand