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# Definite Integrals

The definite integral of a function computes the area under the graph of its curve, allowing us to calculate areas and volumes that are not easily done using geometry alone.

The graph of the function \(y = f(x)\) is shown above. What is the value of \[\int_0^6 f(x) dx?\]

If Morgan uses 2 subintervals, and Pat uses 4 subintervals, whose approximation is closer to the true value of the integral?

Ferb knows that \[\int_0^8 x dx = 32,\] and is interested in how close a right-hand Reimann sum approximation to the integral can be.

Based on his work so far, if Ferb uses 32 subintervals, what will his approximation be?

Number of subintervals | Approximation | Error |

1 | 64 | 32 |

2 | 48 | 16 |

4 | 40 | 8 |

8 | 36 | 4 |

16 | 34 | 2 |

32 | ?? |

Which of the following is true of \(A\) and \(B?\)

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