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

**Q1: **

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

5 | 7 | 9 | 11 | 13 | 15 | 17 | |

0.4 | 1.8 | 2.5 | 3.1 |

**Q2: **

Given that and that , evaluate, to the nearest six decimal places, the Riemann sum for with six subintervals, taking the sample points to be left endpoints.

**Q3: **

Given that and that , evaluate, to the nearest six decimal places, the Riemann sum for with six subintervals, taking the sample points to be left endpoints.

**Q4: **

Given that and that , evaluate, to the nearest six decimal places, the Riemann sum for with six subintervals, taking the sample points to be left endpoints.

**Q5: **

**Q6: **

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

2 | 6 | 10 | 14 | 18 | 22 | 26 | |

0.6 | 1.7 |

**Q7: **

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

3 | 7 | 11 | 15 | 19 | 23 | 27 | |

0.8 | 1.7 | 2.2 |

**Q8: **

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

0.1 | 1.5 | 2.4 | 3.1 |