# Worksheet: Finding Areas Using Midpoint Riemann Sum

In this worksheet, we will practice finding an approximated value of the area under a curve using midpoint approximation.

Q1:

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

Q2:

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

 𝑥 𝑓 ( 𝑥 ) 1 2 3 4 5 6 7 − 3 . 3 − 2 . 1 − 1 . 3 − 0 . 1 0.9 2.1 3.1

Q3:

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

• A7
• B
• C
• D
• E5

Q4:

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

Q5:

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

Q6:

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

Q7:

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

Q8:

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

Q9:

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

Q10:

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

 𝑥 𝑓 ( 𝑥 ) 1 4 7 10 13 16 19 − 3 . 6 − 2 . 1 − 1 . 2 − 0 . 5 0.4 1.2 2

Q11:

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

 𝑥 𝑓 ( 𝑥 ) 1 5 9 13 17 21 25 − 4 − 2 . 7 − 2 − 0 . 8 0.2 0.9 1.5

Q12:

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

 𝑥 𝑓 ( 𝑥 ) 4 5 6 7 8 9 10 − 2 . 9 − 2 . 4 − 1 . 9 − 1 . 1 0.1 1.1 1.7

Q13:

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

Q14:

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

• A38
• B
• C86
• D59
• E

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