Riemann Sum Practice

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)

Tags

CCSS.HSA.SSE.A.1

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

• 28

• 16

• 34

• 21

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.B.6

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 increasing, a right hand Riemann Sum is which of the following:

• Overestimate
• Underestimate
• Unable to Determine
• Exact Solution

Use the function values in the following table and the Trapezoidal Rule with n=6 to approximate the integral from x=0 to x=12.
x:     0     2     4     6      8    10    12  
f(x):  7   11    20   25    18   14     9

• 96
• 102
• 190
• 192

Use the function values in the following table and right reimann sum to approximate the integral from x=0 to x=6 with n=6.
x:      0     1     2     3      4     5      6  
f(x): 12   10    9    11    13   16    18

• 71
• 74
• 77
• 78

Tags

CCSS.HSF.IF.B.4

Use the function values in the following table and left reimann sum to approximate the integral from x=0 to x=6 with n=6.
x:      0     1     2     3      4     5      6  
f(x): 12   10    9    11    13   16    18

• 71
• 74
• 77
• 78

What does this picture represent?

• Left Riemann Sum

• Right Riemann Sum

• Middle Riemann Sum

• Trapezoidal Sum