Calculus
# Definite Integrals

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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