Approximating Areas with Riemann Sums

• 3.75

• 4.5

• 5

• 7

Answer explanation

The Midpoint Rule with 2 subintervals gives an approximation of 4.5 for the area under the curve y = x^3 from x = 1 to x = 2.

• 8

• 10

• 12

• 14

Answer explanation

The Midpoint Rule with 2 subintervals gives an approximation of 10 for the integral of (2x + 1) from 1 to 3.

When calculating the numerical approximation of an integral using the Trapezoidal Rule, which of the following factors does not affect the accuracy of the approximation?

• The smoothness of the function being integrated

• The number of subintervals

• The method used to calculate the function's values at the endpoints of the subintervals

• The color of the graph of the function

Answer explanation

The color of the graph of the function does not affect the accuracy of the Trapezoidal Rule approximation.

What does this picture represent?

• Left Riemann Sum

• Right Riemann Sum

• Middle Riemann Sum

• Trapezoidal Sum

What does picture represent?

• Left Riemann Sum

• Right Riemann Sum

• Middle Riemann Sum

• Trapezoidal Sum

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

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

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

• Overestimate

• Underestimate

• Exact Solution

• Unable to Determine