RAM and the Definite Integral

A Riemann Sum uses rectangles to

• approximate the area under a curve. The more rectangles, the better the approximation.

• approximate the area under a curve. The less rectangles, the better the approximation.

• approximate the area under a curve. The more rectangles, the worse the approximation.

What statement best describes the Riemann Sum?

• 4 intervals, with heights using middle values

• 4 intervals, with heights using left values

• 5 intervals, with heights using middle values

• 5 intervals, with heights using right values

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 increasing, a right hand Riemann Sum is which of the following:

• Overestimate
• Underestimate
• Unable to Determine
• Exact Solution

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)

• positive

• negative

• zero

• The area from the curve to the x-axis from x = a to x = b

• The rate at which f(x) is changing from x = a to x = b

• The area from the curve to the y-axis from x = a to x = b

• The volume when the curve is rotated about the x-axis from x = a to x = b

• -11

• 11

• 9

• not enough information to determine

• -2

• 0

• 20

• not enough information to determine

• -11

• -2

• 20

• not enough information to determine