Three rectangles are used to estimate the area under the curve, y = x^2 + 4, from x = 0 to x = 6. Using the right-hand rectangular approximation method (RRAM), what is the approximate area under the curve for the given interval?
A. 47
B. 64
C. 68
D. 94
E. 136
Four rectangles are used to estimate the area under the curve, y = x^3, from x = 0 to x = 12. Using the left-hand rectangular approximation method (LRAM), what is the approximate area under the curve for the given interval?
A. 972
B. 2,700
C. 2,916
D. 5,022
E. 8,100
Six rectangles are used to estimate the area under the curve, y = −x + 5, from x = 0 to x = 3. Using the midpoint rectangular approximation method (MRAM), what is the approximate area under the curve for the given interval?
A. 9.75
B. 10.5
C. 11.25
D. 21
E. 22.5
The velocity of a drone, during the first minute of flying, is recorded in the table below.
Time (seconds) 0 10 20 30 40 50 60
Velocity (ft./sec) 20 22 26 30 36 34 32
Using the left-hand rectangular approximation method (LRAM), what is the approximate total distance the drone flies during the first minute?
A. 1,480 ft.
B. 1,680 ft.
C. 1,800 ft.
D. 4,780 ft.
E. 6,700 ft.