AP Calc AB Mid-Unit 6

What does picture represent?

• Left Riemann Sum

• Right Riemann Sum

• Middle Riemann Sum

• Trapezoidal Sum

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 decreasing, a trapezoidal approximation will be which of the following:

• Underestimate
• Overestimate
• Exact Solution
• Unable to Determine

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)

Based on the table, use a Right 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)

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

• 14

• 7

• 26

• 11

Use a trapezoidal sum with four intervals from the table to estimate the integral of 0 to 9 of V(t).

• 64

• 67

• 93

• 151/2

• -1
• -2
• 1/2
• -1/2

• 5
• 3
• 1
• 2

Which of the following definite integrals represent the area of the shaded region? (Scaled by ones)

• $\int_0^3\ x^2+3\ dx$

• $\int_1^3\ x^2+3\ dx$

• $\int_3^1\ x^2+3\ dx$

• $\int_1^3x^{2\ }+3\ dy$