Approximating Area

What is the approximate area of the region, using 4 subintervals and heights using left values?

• 7.5

• 7.75

• 10

• 11.5

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

• 14

• 7

• 26

• 11

Integrate:

• x^1/2 + C

• ¹/_(2√x) + C

• ³/₂*x^3/2 + C

• ²/₃*x^3/2 + C

Determine the integral rule of the given expression:

• ^-1/_x² + C

• lnx + C

• ln|x| + C

• ^-1/_x + C

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

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

Based on the table, use a left-hand sum and 4 sub-intervals to estimate the area under the curve. (Choose the correct set-up.) *Hint (consider the height and width of each rectangle)

• 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)

Critical Thinking: Based on the table, use a right-hand sum and 4 sub-intervals to estimate the area under the curve. (Choose the correct set-up.) *Hint (consider the height and width of each rectangle)

• 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)

Estimate the area of the region using two intervals and heights using right values. Then estimate the area using four intervals and heights using right values.

What is the difference between the two estimates?

• 0

• 2.5

• 5.75

• 8