# Worksheet: Midpoint Riemann Sum

Q1:

Let over . Using four subintervals and taking midpoints as sample points, evaluate the Riemann sum of to six decimal places.

Q2:

Let over . Using four subintervals and taking midpoints as sample points, evaluate the Riemann sum of to six decimal places.

Q3:

Using the midpoint rule with , round to four decimal places.

Q4:

Using the midpoint rule with , round to four decimal places.

Q5:

The table shows the values of a function obtained from an experiment. Estimate using three equal subintervals with midpoints.

 π₯ π ( π₯ ) 1 2 3 4 5 6 7 β 3 . 3 β 2 . 1 β 1 . 3 β 0 . 1 0.9 2.1 3.1

Q6:

The table shows the values of a function obtained from an experiment. Estimate using three equal subintervals with midpoints.

 π₯ π ( π₯ ) 1 4 7 10 13 16 19 β 3 . 6 β 2 . 1 β 1 . 2 β 0 . 5 0.4 1.2 2

Q7:

The table shows the values of a function obtained from an experiment. Estimate using three equal subintervals with midpoints.

 π₯ π ( π₯ ) 1 5 9 13 17 21 25 β 4 β 2 . 7 β 2 β 0 . 8 0.2 0.9 1.5

Q8:

The table shows the values of a function obtained from an experiment. Estimate using three equal subintervals with midpoints.

 π₯ π ( π₯ ) 4 5 6 7 8 9 10 β 2 . 9 β 2 . 4 β 1 . 9 β 1 . 1 0.1 1.1 1.7

Q9:

Estimate using the midpoint rule with , giving your answer to four decimal places.

Q10:

Estimate using the midpoint rule with , giving your answer to four decimal places.

Q11:

Estimate using the midpoint rule with , giving your answer to four decimal places.

Q12:

Using the Midpoint Rule with , give an estimate of . Give your answer to four decimal places.

Q13:

Given and , evaluate the Riemann sum for with six subintervals, taking sample points to be midpoints.

• A7
• B
• C
• D
• E5

Q14:

Given and , evaluate the Riemann sum for with six subintervals, taking sample points to be midpoints.

• A38
• B
• C86
• D59
• E