Question

Asked May 10, 2019

approximate the area under the graph of f(x) and above the x-axis using the following methods with n = 4. (a). use left endpoints, (b). use right end points, (c) average the answers in parts (a) and (b). (d) use midpoints.

f(x) = 3x + 2 from x = 1 to x = 3

Step 1

Ypu have asked a question with four sub parts. I have answered the first three sub parts. Please post the balance sub part as separate question.

Width of each rectangle, dx = (x_{2} – x_{1}) / n = (3 – 1) / 4 = 0.50

Step 2

Part (a)

Please see the table below:

x | f(x) = 3x + 2 | f(x).dx = f(x) x 0.5 |

1.00 | 5.00 | 2.50 |

1.50 | 6.50 | 3.25 |

2.00 | 8.00 | 4.00 |

2.50 | 9.50 | 4.75 |

Total Area | 14.50 |

Step 3

Part (b)

Right hand rule:

x | f(x) = 3x + 2 | f(x).dx = f(x) x 0.5 |

1.50 | 6.50 | 3.25 |

2.00 | 8.00 | 4.00 |

2.50 | ... |

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