Chapter 5 Calculus Review

Use a right Riemann Sum to approximate the area of the shaded area.

• 12

• 9

• 10

• 5

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

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

∫ x(x² - 4) dx

• x²/2(x³/3 - 4x) + C
• .25x⁴ -2x² + C
• 3x²- 4 + C
• x⁴ - 4x² + C

∫(4/x - e^x ) dx

• 4ln x - e^x
• 4 ln x + e^x + C
• 4 ln x - e^x + C
• 4/x²  - 4e^x + C

∫(4 - 18x)dx

• F(x) = -18
• F(x) = 4x - 9x²
• F(x) = 4x - 9x² + C
• F(x) = (4 - 18x)² /2 + C

∫ t⁶ dt

• 6t⁵
• 6t⁵ + C
• 1/7 t⁷ + C
• t⁷ + C