Riemann Sums

For a function that is strictly decreasing, a right hand Riemann Sum is which of the following:

• Overestimate
• Underestimate
• Exact Solution
• Unable to Determine

For a function that is strictly decreasing, a trapezoidal approximation will be which of the following:

• Underestimate
• Overestimate
• Exact Solution
• Unable to Determine

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)

Use a midpoint Riemann Sum to approximate the area between 0 to 3 with 3 subintervals.

• 14

• 7

• 26

• 11

Which property of a graph will cause a trapezoidal sum to be an underestimate?

• Increasing

• Decreasing

• Concave up

• Concave down

Which property of a graph will cause a left Riemann sum to be an overestimate?

• Increasing

• Decreasing

• Concave up

• Concave down

Which property of a graph will cause a linear approximation to be an overestimate?

• Increasing

• Decreasing

• Concave up

• Concave down

Integrate

• A
• B
• C
• D

Integrate

• A
• B
• C
• D

A graph represents the rate at which water is draining (in gal/min) from a tub at time t. Which of the following is the best interpretation of the area under the graph?

• The amount of water left in the tub at time t

• The change in height of the water from time t=a to time t=b

• The total amount of water drained from time t=a to time t=b

• The average speed the water is draining from the tank from time t=a to time t=b