Calculus Area Under Curve Riemann Trapezoid

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

If an increasing or decreasing function is concave up, a Trapezoidal approximation is which of the following:

• Underestimate
• Unable to Determine
• Overestimate
• Exact Solution

Using 5 subintervals, calculate the distance traveled using a left sum.

• 360
• 420
• 396
• 390

• 64

• 67

• 93

• underestimate

• overestimate

• exact answer

• Impossible to determine from information given.

The table above gives the level of a person's cholesterol at different times during a 10-week treatment period. What is the level over this 10-week period obtained by using a Trapezoidal approximation with the sub-intervals [0,2] [2,6] and [6,10]

• 1880

• 1930

• 1950

• 1980

On a certain day, the rate at which material is deposited at a recycling center is modeled by the function R, where R(t) is measured in tons per hour and t is the number of hours since the center opened. Using a trapezoidal sum with three sub-intervals indicated by the data in the table, what is the approximate number of tons of material deposited in the first 9 hours since the center opened?

• 68

• 70.5

• 85

• 136