AP Calc AB Practice Problems 4.1-4.3

• A
• B
• C
• D

Find the antiderivative of

f'(x) = x² when f(3) = 11.

• (1/3)x³+ 2

• x³ + 29

• (1/3)x³ + 9

• x³ + 11

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

• 14

• 7

• 26

• 11

Evaluate the definite integral.

• Not possible

Which definite integral models the area highlighted above?

• 
• 
• 
• 

• Positive

• Negative

• 0

• Cannot be determined

• Positive

• Negative

• 0

• Cannot be determined