5.1-5.2 Rieman Sum Equations, Tables, and Applications

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 is the value of the Riemann sum?

• 8

• 10

• 11

• 12

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)

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

• 28

• 16

• 34

• 21

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

• Overestimate
• Underestimate
• Exact Solution
• Unable to Determine

• 96
• 102
• 190
• 192

What does this picture represent?

• Left Riemann Sum

• Right Riemann Sum

• Middle Riemann Sum

• Trapezoidal Sum

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

• 14

• 7

• 26

• 11

• Average Value

• Net Area

• Total Area

• Average Rate of Change

• 176

• 352

• 420

• 488