# 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.

1 | 2 | 3 | 4 | 5 | 6 | 7 | |

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.

1 | 4 | 7 | 10 | 13 | 16 | 19 | |

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.

1 | 5 | 9 | 13 | 17 | 21 | 25 | |

0.2 | 0.9 | 1.5 |

**Q12: **

4 | 5 | 6 | 7 | 8 | 9 | 10 | |

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