Chapter 5.3, Problem 49E

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area.

To determine

The area under the curve

Explanation

**Given information**:

The equation of curve is

The region lies between

**Calculation:**

Find *y* value using the curve function:

Substitute 0 for *x* in Equation (1).

Hence, the co-ordinates

Substitute 1 for *x* in Equation (1).

Hence, the co-ordinates

Similarly calculate for remaining values and are shown in Table (1).

Table (1) shows the co-ordinates of

x | y |

0 | 0.00 |

1 | 1.00 |

2 | 1.26 |

3 | 1.44 |

4 | 1.59 |

5 | 1.71 |

6 | 1.82 |

7 | 1.91 |

8 | 2.00 |

9 | 2.08 |

10 | 2.15 |

11 | 2.22 |

12 | 2.29 |

13 | 2.35 |

14 | 2.41 |

15 | 2.47 |

16 | 2.52 |

17 | 2.57 |

18 | 2.62 |

19 | 2.67 |

20 | 2.71 |

21 | 2.76 |

22 | 2.80 |

23 | 2.84 |

24 | 2.88 |

25 | 2.92 |

26 | 2.96 |

27 | 3.00 |

Draw the diagram for the curve function

Show the diagram for the curve function

Refer to Figure (1).

The rough estimate of area can be obtianed by splitting the region bounded by the curve

The area under the curve is calculated approximately by deducting the area of

Find the rectangular area

Find the traingular area

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P-1RECh-5 P-2RECh-5 P-3RECh-5 P-4RECh-5 P-5RECh-5 P-6RECh-5 P-7RECh-5 P-8RECh-5 P-9RECh-5 P-10RECh-5 P-11RECh-5 P-12RECh-5 P-13RECh-5 P-14RECh-5 P-15RECh-5 P-16RECh-5 P-17RECh-5 P-18RECh-5 P-19RECh-5 P-20RECh-5 P-21RECh-5 P-22RECh-5 P-23RECh-5 P-24RECh-5 P-25RECh-5 P-26RECh-5 P-27RECh-5 P-28RECh-5 P-29RECh-5 P-30RECh-5 P-31RECh-5 P-32RECh-5 P-33RECh-5 P-34RECh-5 P-35RECh-5 P-36RECh-5 P-37RECh-5 P-38RECh-5 P-39RECh-5 P-40RECh-5 P-41RECh-5 P-42RECh-5 P-43RECh-5 P-44RECh-5 P-45RECh-5 P-46RECh-5 P-47RECh-5 P-48RECh-5 P-49RECh-5 P-50RECh-5 P-51RECh-5 P-52RECh-5 P-53RECh-5 P-54RECh-5 P-55RECh-5 P-56RECh-5 P-57RECh-5 P-58RECh-5 P-59RECh-5 P-60RECh-5 P-61RECh-5 P-62RECh-5 P-63RECh-5 P-66RECh-5 P-69RECh-5 P-70RECh-5 P-71RECh-5 P-72RECh-5 P-1PCh-5 P-2PCh-5 P-3PCh-5 P-5PCh-5 P-6PCh-5 P-7PCh-5 P-8PCh-5 P-9PCh-5 P-10PCh-5 P-11PCh-5 P-14PCh-5 P-15PCh-5 P-18PCh-5 P-19P

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