**QUESTION**

The table gives the values of a function obtained from an experiment. Use them to estimate

9 |
f(x) dx |

3 |

using three equal subintervals with right endpoints, left endpoints, and midpoints.

x |
3 | 4 | 5 | 6 | 7 | 8 | 9 |

f(x) |
−3.5 | −2.3 | −0.5 | 0.2 | 0.9 | 1.5 | 1.9 |

(a) Estimate

9 |
f(x) dx |

3 |

using three equal subintervals with right endpoints.

*R*_{3} =

If the function is known to be an increasing function, can you say
whether your estimate is less than or greater than the exact value
of the integral?

less thangreater than one cannot say

(b) Estimate

9 |
f(x) dx |

3 |

using three equal subintervals with left endpoints.

*L*_{3} =

If the function is known to be an increasing function, can you say
whether your estimate is less than or greater than the exact value
of the integral?

less thangreater than one cannot say

(c) Estimate

9 |
f(x) dx |

3 |

using three equal subintervals with midpoints.

*M*_{3} =

If the function is known to be an increasing function, can you say
whether your estimate is less than or greater than the exact value
of the integral?

less thangreater than one cannot say